C3xC3

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

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