Author: John Murray

Title: Components of the involution module in blocks with cyclic or Klein-four defect group

Abstract: Each $p$-block of a finite group has an associated
defect group, which is a $p$-subgroup of the group.
Each real $2$-block has, in addition, an associated
{\em extended defect group}, which is is a $2$-subgroup
of the group that contains a defect group as a subgroup
of index $\leq 2$.
We consider the possible extended defect groups of a real
$2$-block that has a cyclic or a Klein-four defect group.
In each case we describe the modules in the block that are
components in the permutation module of the group acting by
conjugation on its involutions.
We also determine the Frobenius-Schur indicators
of the irreducible characters in the block.

Status: submitted for publication