Characters, bilinear forms and solvable groups

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• 作者：John C. Murray^a ; ^{John.Murray@maths.nuim.ie" class="auth_mail" title="E-mail the corresponding author} ; Gabriel Navarro^b ; ^{Gabriel.Navarro@uv.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Finite solvable group ; Frobenius&ndash ; Schur indicator ; Brauer character ; Bilinear form
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：449
• 期：Complete
• 页码：346-354
• 全文大小：295 K

文摘

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.