Semicharacters of Groups

DOI10.1080/00927872.2013.879162zbMATH Open1328.20046arXiv1112.6125OpenAlexW2034478450MaRDI QIDQ5256700

Gil Alon

Publication date: 19 June 2015

Published in: Communications in Algebra (Search for Journal in Brave)

Abstract: We define the notion of a semicharacter of a group G : A function from the group to C*, whose restriction to any abelian subgroup is a homomorphism. We conjecture that for any finite group, the order of the group of semicharacters is divisible by the order of the group. We prove that the conjecture holds for some important families of groups, including the Symmetric groups and the groups GL(2,q).

Full work available at URL: https://arxiv.org/abs/1112.6125

zbMATH Keywords

symmetric groupsSylow subgroupsalternating groupslinear groupstriangular groupsgroups of semicharacterssemicharacters of finite groups

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Ordinary representations and characters (20C15) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Automorphisms of abstract finite groups (20D45) Abstract finite groups (20D99)

Cites Work

• The Sylow 2-subgroups of the finite classical groups
• Composition Factors from the Group Ring and Artin's Theorem on Orders of Simple Groups

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