The number of simple modules of the block with a hyperfocal subgroup which is \(C_{2^n}\times C_{2^n}\)

Xueqin Hu (Central China Normal University)

Frank Adams 1,

In this talk, we will investigate the block with a hyperfocal subgroup which is \(C_{2^n}\times C_{2^n}\). It is motivated by the work of Watanabe which is about the block with a cyclic hyperfocal subgroup. We will calculate the number of simple modules of the block under our setting. There are two different cases with respect to the two different Brauer category of the block with a hyperfocal subgroup which is \(C_{2^n}\times C_{2^n}\). In one case, we will show that the number is \(3\). In the other case, it is proved that the number is \(2\) under the restriction on the order of the hyperfocal subgroup. This is a joint work with Yuanyang Zhou.

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