On the isomorphism of unitary subgroups of noncommutative group algebras

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Let F G be the group algebra of a finite p-group G over a field F of characteristic p. Let ⊛ be an involution of the group algebra F G which arises form the group basis G. The upper bound for the number of non-isomorphic ⊛-unitary subgroups is the number of conjugacy classes of the automorphism group G with all the elements of order two. The upper bound is not always reached in the case when G is an abelian group, but for non-abelian case the question is open. In this paper we present a non-abelian p-group G whose group algebra F G has sharply less number of non-isomorphic ⊛-unitary subgroups than the given upper bound.

Original languageEnglish
Pages (from-to)115-122
Number of pages8
JournalJournal of Algebra Combinatorics Discrete Structures and Applications
Issue number2
Publication statusPublished - May 13 2022


  • Group of units
  • Group ring
  • Unitary subgroup

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics


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