On units of twisted group algebras

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Abstract

We study units of twisted group algebras. Let G be a finite group and K be a field of characteristic p > 0. Assume that K is not algebraic over a finite field. We determine when units of Kt[G] do not contain any nonabelian free subgroup. We also discuss what will happen when G is locally finite. For twisted group algebras of locally finite groups over any infinite field of characteristic p > 0, we characterize those twisted group algebras with units satisfying a group identity. Finally, we include a new characterization for twisted group algebras to satisfy a polynomial identity.

Original languageEnglish
Pages (from-to)271-282
Number of pages12
JournalJournal of Algebra
Volume250
Issue number1
DOIs
Publication statusPublished - 2002 Apr 1

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Keywords

  • Free subgroups
  • Group identities
  • Polynomial identities
  • Twisted group algebras
  • Units

ASJC Scopus subject areas

  • Algebra and Number Theory

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