Products of Metacyclic Groups

Sambale, Benjamin

doi:10.1007/978-3-319-12006-5_9

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Proof Of Theorem 111

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2023

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“…Since B is not nilpotent, there exists a so-called essential subgroup in the fusion system of B . Then Q is a Klein four-group and there exists a unique B -subpair (see [37, Theorem 1]). Moreover, is nilpotent with defect group (see [1, Theorem IV.3.19]).…”

Section: Proof Of Theorem 11mentioning

confidence: 99%

Real Blocks With Dihedral Defect Groups Revisited

Sambale

2023

Bull. Aust. Math. Soc.

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The Frobenius–Schur indicators of characters in a real $2$ -block with dihedral defect groups have been determined by Murray [‘Real subpairs and Frobenius–Schur indicators of characters in 2-blocks’, J. Algebra322 (2009), 489–513]. We show that two infinite families described in his work do not exist and we construct examples for the remaining families. We further present some partial results on Frobenius–Schur indicators of characters in other tame blocks.

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