Semicharacters of Groups

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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).

Original languageEnglish
Pages (from-to)1771-1783
Number of pages13
JournalCommunications in Algebra
Issue number5
StatePublished - 4 May 2015

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