Abstract
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 language | English |
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Pages (from-to) | 115-122 |
Number of pages | 8 |
Journal | Journal of Algebra Combinatorics Discrete Structures and Applications |
Volume | 9 |
Issue number | 2 |
DOIs | |
Publication status | Published - May 13 2022 |
Keywords
- Group of units
- Group ring
- Unitary subgroup
ASJC Scopus subject areas
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics