C3xC3

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Blocks with defect group [math]C_3 \times C_3[/math]

Under-construction.png

Source algebra equivalence classes of principal blocks with this defect group have been classified by Koshitani in [Ko03] using the CFSG.


The numerical invariants of arbitrary blocks with defect group [math]C_3 \times C_3[/math] were calculated for all inertial quotients except [math]C_8[/math] and [math]Q_8[/math] by Kiyota in [Ki84], and these cases remain an open problem. These calculations do not involve the CFSG.

CLASSIFICATION INCOMPLETE
Class Representative # lifts / [math]\mathcal{O}[/math] [math]k(B)[/math] [math]l(B)[/math] Inertial quotients [math]{\rm Pic}_\mathcal{O}(B)[/math] [math]{\rm Pic}_k(B)[/math] [math]{\rm mf_\mathcal{O}(B)}[/math] [math]{\rm mf_k(B)}[/math] Notes
M(9,2,1) [math]k(C_3 \times C_3)[/math] 1 9 1 [math]1[/math] [math](C_3 \times C_3):GL_2(3)[/math] 1 1