References

A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T U, V, W, X, Y, Z,

[Al79]	J. L. Alperin, Projective modules for [math]SL(2,2^n)[/math], J. Pure and Applied Algebra 15 (1979), 219-234.
[Al80]	J. L. Alperin, Local representation theory, The Santa Cruz Conference on Finite Groups., Proc. Sympos. Pure Math. 37 (1980), 369-375.
[AE81]	J. L. Alperin and L. Evens, Representations, resoluutions and Quillen's dimension theorem, J. Pure Appl. Algebra 22 (1981), 1-9.
[AE04]	Jianbei An and C. W. Eaton, Blocks with trivial intersection defect groups, Math. Z. 247 (2004), 461-486.
[AE04]	Jianbei An and C. W. Eaton, Morita equivalence classes of blocks with extraspecial defect groups [math]p_+^{1+2}[/math], arxiv:2310.02150
[Ar19]	C. G. Ardito, Morita equivalence classes of blocks with elementary abelian defect groups of order 32, J. Algebra 573 (2021), 297-335.
[ArMcK20]	C. G. Ardito and E. McKernon, 2-blocks with an abelian defect group and a freely acting cyclic inertial quotient, arxiv.org/abs/2010.08329
[AS20]	C. G. Ardito and B. Sambale, Broué's Conjecture for 2-blocks with elementary abelian defect groups of order 32, Advances in Group Theory and Applications 12 (2021), 71–78.
[AKO11]	M. Aschbacher, R. Kessar and B. Oliver, Fusion systems in algebra and topology, London Mathematical Society Lecture Notes 391, Cambridge University Press (2011).
[BK07]	D. Benson and R. Kessar, Blocks inequivalent to their Frobenius twists, J. Algebra 315 (2007), 588-599.
[BS23]	D. Benson and B. Sambale, Finite dimensional algebras not arising as blocks in group algebras, arxiv:2301.10537
[BKL18]	R. Boltje, R. Kessar, and M. Linckelmann, On Picard groups of blocks of finite groups, J. Algebra 558 (2020), 70-101.
[Bra41]	R. Brauer, Investigations on group characters, Ann. Math. 42 (1941), 936-958.
[BP80]	M. Broué and L. Puig, A Frobenius theorem for blocks, Invent. Math. 56 (1980), 117-128.
[BP80b]	M. Broué and L. Puig, Characters and local structure in G-algebras, J. Algebra 63 (1980), 306-317.
[Cr11]	D. A. Craven, The Theory of Fusion Systems: An Algebraic Approach, Cambridge University Press (2011).
[Cr12]	D. A. Craven, Perverse Equivalences and Broué's Conjecture II: The Cyclic Case, arXiv:1207.0116
[CDR18]	D. A. Craven, O. Dudas and R. Rouquier, The Brauer trees of unipotent blocks, to appear, J. EMS, arXiv:1701.07097
[CEKL11]	D. A. Craven, C. W. Eaton, R. Kessar and M. Linckelmann, The structure of blocks with a Klein four defect group, Math. Z. 268 (2011), 441-476.
[CG12]	D. A. Craven and A. Glesser, Fusion systems on small p-groups, Trans. AMS 364 (2012) 5945-5967.
[CR13]	D. A. Craven and R. Rouquier, Perverse equivalences and Broué's conjecture, Adv. Math. 248 (2013), 1-58.
[CuRe81a]	C. W. Curtis and I. Reiner, Methods of representation theory, with applications to finite groups and orders, Volume I, Wiley-Interscience (1981).
[CuRe81b]	C. W. Curtis and I. Reiner, Methods of representation theory, with applications to finite groups and orders, Volume II, Wiley-Interscience (1981).
[Da66]	E. C. Dade, Blocks with cyclic defect groups, Ann. Math. 84 (1966), 20-48.
[DE20]	S. Danz and K. Erdmann, On Ext-Quivers of Blocks of weight two for symmetric groups, arXiv:2008.10999
[Du14]	O. Dudas, Coxeter orbits and Brauer trees II, Int. Math. Res. Not. 15 (2014), 4100-4123.
[Dü04]	O. Düvel, On Donovan's conjecture, J. Algebra 272 (2004), 1-26.
[Ea16]	C. W. Eaton, Morita equivalence classes of [math]2[/math]-blocks of defect three, Proc. AMS 144 (2016), 1961-1970.
[Ea18]	C. W. Eaton, Morita equivalence classes of blocks with elementary abelian defect groups of order 16, arXiv:1612.03485
[Ea24]	C. W. Eaton, Blocks whose defect groups are Suzuki 2-groups, arXiv:2401.04028
[EEL18]	C. W. Eaton, F. Eisele and M. Livesey, Donovan's conjecture, blocks with abelian defect groups and discrete valuation rings, Math. Z. 295 (2020), 249-264.
[EKKS14]	C. W. Eaton, R. Kessar, B. Külshammer and B. Sambale, [math]2[/math]-blocks with abelian defect groups, Adv. Math. 254 (2014), 706-735.
[EKS12]	C. W. Eaton, B. Külshammer and B. Sambale, [math]2[/math]-blocks with minimal nonabelian defect groups, II, J. Group Theory 15 (2012), 311-321.
[EL18a]	C. W. Eaton and M. Livesey, Classifying blocks with abelian defect groups of rank 3 for the prime 2, J. Algebra 515 (2018), 1-18.
[EL18b]	C. W. Eaton and M. Livesey, Donovan's conjecture and blocks with abelian defect groups, Proc. AMS. 147 (2019), 963-970.
[EL18c]	C. W. Eaton and M. Livesey, Some examples of Picard groups of blocks, J. Algebra 558 (2020), 350-370.
[EL20]	C. W. Eaton and M. Livesey, Donovan's conjecture and extensions by the centralizer of a defect group, J. Algebra 582 (2021), 157-176.
[EL23]	C. W. Eaton and M. Livesey, Morita equivalence classes of [math]2[/math]-blocks with abelian defect groups of rank [math]4[/math], arxiv:2310.05734, to appear, J. LMS
[Ei16]	F. Eisele, Blocks with a generalized quaternion defect group and three simple modules over a [math]2[/math]-adic ring, J. Algebra 456 (2016), 294-322.
[Ei18]	F. Eisele, The Picard group of an order and Külshammer reduction, Algebr. Represent. Theory 24 (2021), 505-518.
[Ei19]	F. Eisele, On the geometry of lattices and finiteness of Picard groups, J. Reine Angew. Math. 782 (2022), 219-333.
[EiLiv20]	F. Eisele and M. Livesey, Arbitrarily large Morita Frobenius numbers, Algebra Number Theory 16 (2022), 1889-1904.
[Er82]	K. Erdmann, Blocks whose defect groups are Klein four groups: a correction, J. Algebra 76 (1982), 505-518.
[Er87]	K. Erdmann, Algebras and dihedral defect groups, Proc. LMS 54 (1987), 88-114.
[Er88a]	K. Erdmann, Algebras and quaternion defect groups, I, Math. Ann. 281 (1988), 545-560.
[Er88b]	K. Erdmann, Algebras and quaternion defect groups, II, Math. Ann. 281 (1988), 561-582.
[Er88c]	K. Erdmann, Algebras and semidihedral defect groups I, Proc. LMS 57 (1988), 109-150.
[Er90]	K. Erdmann, Blocks of tame representation type and related algebras, Lecture Notes in Mathematics 1428, Springer-Verlag (1990).
[Er90b]	K. Erdmann, Algebras and semidihedral defect groups II, Proc. LMS 60 (1990), 123-165.
[Fa17]	N. Farrell, On the Morita Frobenius numbers of blocks of finite reductive groups, J. Algebra 471 (2017), 299-318.
[FK18]	N. Farrell and R. Kessar, Rationality of blocks of quasi-simple finite groups, Represent. Theory 23 (2019), 325-349.
[GMdelR21]	D. Garcia, l. Margolis and A. del Rio, Non-isomorphic 2-groups with isomorphic modular group algebras, J. Reine Angew. Math. f783 (2022), 269–274.
[GO97]	H. Gollan and T. Okuyama, Derived equivalences for the smallest Janko group, preprint (1997).
[GT19]	R. M. Guralnick and Pham Huu Tiep, Sectional rank and Cohomology, J. Algebra (2019) https://doi.org/10.1016/j.jalgebra.2019.04.023
[HM07]	G. T. Helleloid and U. Martin, The automorphism group of a finite [math]p[/math]-group is almost always a [math]p[/math]-group, J. Algebra (2007), 294-329.
[HP94]	H-W. Henn and S. Priddy, [math]p[/math]-nilpotence, classifying space indecompsability, and other properties of almost finite groups, Comment. Math. Helvetici (1994), 335-350.
[Hi63]	G. Higman, Suzuki 2-groups, Illinois J. Math. 7 (1963), 79–96.
[HK00]	G. Hiss and R. Kessar, Scopes reduction and Morita equivalence classes of blocks in finite classical groups, J. Algebra 230 (2000), 378-423.
[HK05]	G. Hiss and R. Kessar, Scopes reduction and Morita equivalence classes of blocks in finite classical groups II, J. Algebra 283 (2005), 522-563.
[Ho97]	T. Holm, Derived equivalent tame blocks, J. Algebra 194 (1997), 178-200.
[HKL07]	T. Holm, R. Kessar and M. Linckelmann, Blocks with a quaternion defect group over a 2-adic ring: the case [math]\tilde{A}_4[/math], Glasgow Math. J. 49 (2007), 29–43.
[Ja69]	G. Janusz, Indecomposable modules for finite groups, Ann. Math. 89 (1969), 209-241.
[Jo96]	T. Jost, Morita equivalences for blocks of finite general linear groups, Manuscripta Math. 91 (1996), 121-144.
[Ke96]	R. Kessar, Blocks and source algebras for the double covers of the symmetric and alternating groups, J. Algebra 186 (1996), 872-933.
[Ke00]	R. Kessar, Equivalences for blocks of the Weyl groups, Proc. Amer. Math. Soc. 128 (2000), 337-346.
[Ke01]	R. Kessar, Source algebra equivalences for blocks of finite general linear groups over a fixed field, Manuscripta Math. 104 (2001), 145-162.
[Ke02]	R. Kessar, Scopes reduction for blocks of finite alternating groups, Quart. J. Math. 53 (2002), 443-454.
[Ke05]	R. Kessar, A remark on Donovan's conjecture, Arch. Math (Basel) 82 (2005), 391-394.
[KL18]	R. Kessar and M. Linckelmann, Descent of equivalences and character bijections, arXiv:1705.07227
[Ki84]	M. Kiyota, On 3-blocks with an elementary abelian defect group of order 9, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 31 (1984), 33–58.
[Ko03]	S. Koshitani, Conjectures of Donovan and Puig for principal [math]3[/math]-blocks with abelian defect groups, Comm. Alg. 31 (2003), 2229-2243; Corrigendum, 32 (2004), 391-393.
[KKW02]	S. Koshitani, N. Kunugi and K. Waki, Broué's conjecture for non-principal 3-blocks of finite groups, J. Pure and Applied Algebra 173 (2002), 177-211.
[KKW04]	S. Koshitani, N. Kunugi and K. Waki, Broué's abelian defect group conjecture for Held group and the sporadic Suzuki group, J. Algebra 279 (2004), 638-666.
[KoLa20]	S. Koshitani and C. Lassueur, Splendid Morita equivalences for principal 2-blocks with dihedral defect groups, Math. Z. 294 (2020), 639-666.
[KoLa20b]	S. Koshitani and C. Lassueur, Splendid Morita equivalences for principal blocks with generalised quaternion defect groups, J. Algebra 558 (2020), 523-533.
[KoLaSa22]	S. Koshitani, C. Lassueur and B. Sambale, Splendid Morita equivalences for principal blocks with semidihedral defect groups, Proceedings of the American Mathematical Society 150 (2022), 41-53.
[KoLaSa23]	S. Koshitani, C. Lassueur and B. Sambale, Principal [math]2[/math]-blocks with wreathed defect groups up to splendid Morita equivalence, arxiv:2310.13621
[Kü80]	B. Külshammer, On 2-blocks with wreathed defect groups, J. Algebra 64 (1980), 529–555.
[Kü81]	B. Külshammer, On p-blocks of p-solvable groups, Comm. Alg. 9 (1981), 1763-1785.
[Kü91]	B. Külshammer, Group-theoretical descriptions of ring-theoretical invariants of group algebras, in Representation Theory of Finite Groups and Finite-Dimensional Algebras (Bielefeld, 1991), Progr. Math. 95, pp. 425-442, Birkhauser (1991).
[Kü95]	B. Külshammer, Donovan's conjecture, crossed products and algebraic group actions, Israel J. Math. 92 (1995), 295-306.
[KS13]	B. Külshammer and B. Sambale, The 2-blocks of defect 4, Representation Theory 17 (2013), 226-236.
[Ku00]	N. Kunugi, Morita equivalent 3-blocks of the 3-dimensional projective special linear groups, Proc. LMS 80 (2000), 575-589.
[Kup69]	H. Kupisch, Unzerlegbare Moduln endlicher Gruppen mit zyklischer p-Sylow Gruppe, Math. Z. 108 (1969), 77-104.
[LM80]	P. Landrock and G. O. Michler, Principal 2-blocks of the simple groups of Ree type, Trans. AMS 260 (1980), 83-111.
[Li94]	M. Linckelmann, The source algebras of blocks with a Klein four defect group, J. Algebra 167 (1994), 821-854.
[Li94b]	M. Linckelmann, A derived equivalence for blocks with dihedral defect groups, J. Algebra 164 (1994), 244-255.
[Li96]	M. Linckelmann, The isomorphism problem for cyclic blocks and their source algebras, Invent. Math. 125 (1996), 265-283.
[Li18]	M. Linckelmann, The strong Frobenius numbers for cyclic defect blocks are equal to one, arXiv:1805.08884
[Li18b]	M. Linckelmann, Finite-dimensional algebras arising as blocks of finite group algebras, Contemporary Mathematics 705 (2018), 155-188.
[Li18c]	M. Linckelmann, The block theory of finite group algebras, Volume 1, London Math. Soc. Student Texts 92, Cambridge University Press (2018).
[Li18d]	M. Linckelmann, The block theory of finite group algebras, Volume 2, London Math. Soc. Student Texts 92, Cambridge University Press (2018).
[LM20]	M. Linckelmann and W. Murphy, A 9-dimensional algebra which is not a block of a finite group, Quarterly Journal of Mathematics 72 (2021), 1077–1088
[Liv19]	M. Livesey, On Picard groups of blocks with normal defect groups, J. Algebra 566 (2021), 94-118.
[LiMa20]	M. Livesey and C. Marchi, On Picent for blocks with normal defect group, arXiv:2002.10571
[LiMa20b]	M. Livesey and C. Marchi, Picard groups for blocks with normal defect groups and linear source bimodules, arXiv:2008.05857
[Mac]	N. Macgregor, Morita equivalence classes of tame blocks of finite groups, J. Algebra 608 (2022), 719-754.
[Mar]	C. Marchi, Picard groups for blocks, PhD thesis, University of Manchester (2022)
[Ma86]	U. Martin, Almost all [math]p[/math]-groups have automorphism group a [math]p[/math]-group, Bull. AMS 15 (1986), 78-82.
[McK19]	E. McKernon, 2-Blocks whose defect group is homocyclic and whose inertial quotient contains a Singer cycle, J. Algebra 563 (2020), 30–48.
[MS08]	J. Müller and M. Schaps, The Broué conjecture for the faithful 3-blocks of [math]4.M_{22}[/math], J. Algebra 319 (2008), 3588-3602.
[NS18]	G. Navarro and B. Sambale, On the blockwise modular isomorphism problem, Manuscripta Math. 157 (2018), 263-278.
[Ne02]	G. Nebe, Group rings of finite groups over p-adic integers, some examples, Proceedings of the conference Around Group rings (Edmonton) Resenhas 5 (2002), 329-350.
[Ok97]	T. Okuyama, Some examples of derived equivalent blocks of finite groups, preprint (1997).
[Pu88]	L. Puig, Nilpotent blocks and their source algebras, Invent. Math. 93 (1988), 77-116.
[Pu94]	L. Puig, On Joanna Scopes’ criterion of equivalence for blocks of symmetric groups, Algebra Colloq. 1 (1994), 25-55.
[Pu99]	L. Puig, On the local structure of Morita and Rickard equivalences between Brauer blocks, Progress in Math. 178, Birkhauser Verlag (1999).
[Pu09]	L. Puig, Block source algebras in p-solvable groups, Michigan Math. J. 58 (2009), 323-338.
[Ri96]	J. Rickard, Splendid equivalences: derived categories and permutation modules, Proc. London Math. Soc. 72 (1996), 331-358.
[Ro95]	R. Rouquier, From stable equivalences to Rickard equivalences for blocks with cyclic defect, Proceedings of Groups 1993, Galway-St. Andrews Conference, Vol. 2, London Math. Soc. Lecture Note Ser. 212, Cambridge University Press (1995), 512-523.
[Ru11]	P. Ruengrot, Perfect isometry groups for blocks of finite groups, PhD Thesis, University of Manchester (2011).
[Sa11]	B. Sambale, [math]2[/math]-blocks with minimal nonabelian defect groups, J. Algebra 337 (2011), 261–284.
[Sa12]	B. Sambale, Blocks with defect group [math]D_{2^n} \times C_{2^m}[/math], J. Pure Appl. Algebra 216 (2012), 119–125.
[Sa12b]	B. Sambale, Fusion systems on metacyclic 2-groups, Osaka J. Math. 49 (2012), 325–329.
[Sa13]	B. Sambale, Blocks with defect group [math]Q_{2^n} \times C_{2^m}[/math] and [math]SD_{2^n} \times C_{2^m}[/math], Algebr. Represent. Theory 16 (2013), 1717–1732.
[Sa13b]	B. Sambale, Blocks with central product defect group [math]D_{2^n} ∗ C_{2^m}[/math], Proc. Amer. Math. Soc. 141 (2013), 4057–4069.
[Sa13c]	B. Sambale, Further evidence for conjectures in block theory, Algebra Number Theory 7 (2013), 2241–2273.
[Sa14]	B. Sambale, Blocks of Finite Groups and Their Invariants, Lecture Notes in Mathematics, Springer (2014).
[Sa16]	B. Sambale, 2-blocks with minimal nonabelian defect groups III, Pacific J. Math. 280 (2016), 475–487.
[Sa20]	B. Sambale, Blocks with small-dimensional basic algebra, Bul. Aust. Math. Soc. 103 (2021), 461-474.
[SSS98]	M. Schaps, D. Shapira and O. Shlomo, Quivers of blocks with normal defect groups, Proc. Symp. in Pure Mathematics 63, Amer. Math. Soc. (1998), 497-510.
[Sc91]	J. Scopes, Cartan matrices and Morita equivalence for blocks of the symmetric groups, J. Algebra 142 (1991), 441-455.
[Sh20]	V. Shalotenko, Bounds on the dimension of Ext for finite groups of Lie type, J. Algebra 550 (2020), 266-289.
[St02]	R. Stancu, Almost all generalized extraspecial p-groups are resistant, J. Algebra 249 (2002), 120-126.
[St06]	R. Stancu, Control of fusion in fusion systems, J. Algebra and its Applications 5 (2006), 817-837.
[Th93]	J. Thévenaz, Most finite groups are [math]p[/math]-nilpotent, Exposition. Math. 11 (1993), 359-363.
[vdW91]	R. van der Waall, On p-nilpotent forcing groups, Indag. Mathem., N.S., 2 (1991), 367-384.
[Wa00]	A. Watanabe, A remark on a splitting theorem for blocks with abelian defect groups, RIMS Kokyuroku 1140, Edited by H.Sasaki, Research Institute for Mathematical Sciences, Kyoto University (2000), 76-79.
[WZZ18]	Chao Wu, Kun Zhang and Yuanyang Zhou, Blocks with defect group [math]Z_{2^n} \times Z_{2^n} \times Z_{2^m}[/math], J. Algebra 510 (2018), 469-498.