Unitary and Symmetric Units of a Commutative Group Algebra

V. A. Bovdi, A. N. Grishkov

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Let F be a field of characteristic two and G a finite abelian 2-group with an involutory automorphism η. If G = H × D with non-trivial subgroups H and D of G such that η inverts the elements of H (H without a direct factor of order 2) and fixes D element-wise, then the linear extension of η to the group algebra FG is called a nice involution. This determines the groups of unitary and symmetric normalized units of FG. We calculate the orders and the invariants of these subgroups.

Original languageEnglish
Pages (from-to)641-654
Number of pages14
JournalProceedings of the Edinburgh Mathematical Society
Volume62
Issue number3
DOIs
Publication statusPublished - Aug 1 2019

Keywords

  • commutative ring
  • group ring
  • involution
  • symmetric element
  • unitary group

ASJC Scopus subject areas

  • Mathematics(all)

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