On units of twisted group algebras

Chia Hsin Liu

doi:10.1006/jabr.2001.9088

On units of twisted group algebras

Chia Hsin Liu^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 K^t[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 language	English
Pages (from-to)	271-282
Number of pages	12
Journal	Journal of Algebra
Volume	250
Issue number	1
DOIs	https://doi.org/10.1006/jabr.2001.9088
Publication status	Published - 2002 Apr 1
Externally published	Yes

Keywords

Free subgroups
Group identities
Polynomial identities
Twisted group algebras
Units

ASJC Scopus subject areas

Algebra and Number Theory

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10.1006/jabr.2001.9088

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AB - 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.

KW - Free subgroups

KW - Group identities

KW - Polynomial identities

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KW - Units

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On units of twisted group algebras

Abstract

Keywords

ASJC Scopus subject areas

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