### Abstract

Let K[G] be the group algebra of a group G over a field K, and let U(K[G]) be its group of units. A conjecture by Brian Hartley asserts that if G is a torsion group and U(K[G]) satisfies a group identity, then K[G] satisfies a polynomial identity. This was verified earlier in case K is an infinite field. Here we modify the original proof so that it handles fields of all sizes.

Original language | English |
---|---|

Pages (from-to) | 327-336 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 127 |

Issue number | 2 |

Publication status | Published - 1999 Dec 1 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*127*(2), 327-336.

**Group algebras with units satisfying a group identity.** / Liu, Chia-Hsin.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 127, no. 2, pp. 327-336.

}

TY - JOUR

T1 - Group algebras with units satisfying a group identity

AU - Liu, Chia-Hsin

PY - 1999/12/1

Y1 - 1999/12/1

N2 - Let K[G] be the group algebra of a group G over a field K, and let U(K[G]) be its group of units. A conjecture by Brian Hartley asserts that if G is a torsion group and U(K[G]) satisfies a group identity, then K[G] satisfies a polynomial identity. This was verified earlier in case K is an infinite field. Here we modify the original proof so that it handles fields of all sizes.

AB - Let K[G] be the group algebra of a group G over a field K, and let U(K[G]) be its group of units. A conjecture by Brian Hartley asserts that if G is a torsion group and U(K[G]) satisfies a group identity, then K[G] satisfies a polynomial identity. This was verified earlier in case K is an infinite field. Here we modify the original proof so that it handles fields of all sizes.

UR - http://www.scopus.com/inward/record.url?scp=33646987603&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646987603&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33646987603

VL - 127

SP - 327

EP - 336

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -