Characters, bilinear forms and solvable groups

JOURNAL OF ALGEBRA

卷:449

Article

Murray, John C.¹  Navarro, Gabriel² 

[1] Natl Univ Ireland Maynooth, Dept Math & Stat, Maynooth, Kildare, Ireland

[2] Univ Valencia, Dept Algebra, Burjassot 46100, Valencia, Spain

关键词: Finite solvable group;    Frobenius-Schur indicator;    Brauer character;    Bilinear form;   

DOI  :  10.1016/j.jalgebra.2015.10.024

来源: Elsevier

【 摘 要 】

We prove a number of results about the ordinary and Brauer characters of finite solvable groups in characteristic 2, by defining and using the concept of the extended nucleus of a real irreducible character. In particular we show that the Isaacs canonical lift of a real irreducible Brauer character has Frobenius-Schur indicator +1. We also show that the principal indecomposable module corresponding to a real irreducible Brauer character affords a quadratic geometry if and only if each extended nucleus is a split extension of a nucleus. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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