C25

Blocks with defect group [math]C_{25}[/math]

These are blocks with cyclic defect groups and so they are described by Brauer trees.

There are 12 possible Brauer trees. It is not known which give rise to [math]\mathcal{O}[/math]-Morita equivalence classes.

CLASSIFICATION INCOMPLETE

Class	Representative	[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
[math]M(25,1,1)[/math]	[math]kC_{25}[/math]	25	1	[math]1[/math]	[math]C_{25} : C_{20}[/math]		1	1
[math]M(25,1,2)[/math]	[math]kD_{50}[/math]	14	2	[math]C_2[/math]			1	1
[math]M(25,1,3)[/math]	[math]B_0(kPSL_2(49))[/math]	14	2	[math]C_2[/math]			1	1
[math]M(25,1,4)[/math]	[math]k(C_{25}:C_4)[/math]	10	4	[math]C_4[/math]	[math]C_4[/math]		1	1
[math]M(25,1,5)[/math]	[math]B_0(kSz(32))[/math]	10	4	[math]C_4[/math]			1	1

Blocks in [math]M(25,1,2)[/math] are derived equivalent (over [math]\mathcal{O}[/math]) to those in [math]M(25,1,3)[/math].

Blocks in [math]M(25,1,4)[/math] are derived equivalent (over [math]\mathcal{O}[/math]) to those in [math]M(25,1,5)[/math].