### 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 | |

Publication status | Published - 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

### Cite this

*Journal of Algebra*,

*250*(1), 271-282. https://doi.org/10.1006/jabr.2001.9088

**On units of twisted group algebras.** / Liu, Chia Hsin.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 250, no. 1, pp. 271-282. https://doi.org/10.1006/jabr.2001.9088

}

TY - JOUR

T1 - On units of twisted group algebras

AU - Liu, Chia Hsin

PY - 2002/4/1

Y1 - 2002/4/1

N2 - 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.

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

KW - Twisted group algebras

KW - Units

UR - http://www.scopus.com/inward/record.url?scp=0036540057&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036540057&partnerID=8YFLogxK

U2 - 10.1006/jabr.2001.9088

DO - 10.1006/jabr.2001.9088

M3 - Article

AN - SCOPUS:0036540057

VL - 250

SP - 271

EP - 282

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -