Strongly real 2-blocks and the Frobenius-Schur indicator.
Osaka Journal of Mathematics, 43.
Let G be a nite group. In this paper we investigate the permutation module of G
acting by conjugation on its involutions, over a eld of characteristic 2. This develops
the main theme of  and . In the former paper G. R. Robinson considered the
projective components of this module. In the latter paper the author showed that each
such component is irreducible and self-dual and belongs to a 2-blocks of defect zero. Here
we investigate which 2-blocks have a composition factor in the involution module. There
are two apparently dierent ways of characterising such blocks. One method is local
and uses the defect classes of the block. This gives rise to the denition of a strongly
real 2-block. The other method is global and uses the Frobenius-Schur indicators of the
irreducible characters in the block. Our main result is Theorem 2. The proof of this
theorem requires Corollaries 4, 15, 18 and 20.
||Real 2-blocks; Frobenius-Schur indicator;
||Faculty of Science and Engineering > Mathematics and Statistics
Dr. John Murray
||07 Oct 2010 11:32
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||Osaka Journal of Mathematics
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