Chin, Angelina Yan Mui
(2022)
*A note on group rings with trivial units.*
Bulletin of The Australian Mathematical Society, 105 (2).
pp. 243-247.
ISSN 0004-9727,
DOI https://doi.org/10.1017/S0004972721000563.

## Abstract

Let R be a ring with identity of characteristic two and G a nontrivial torsion group. We show that if the units in the group ring RG are all trivial, then G must be cyclic of order two or three. We also consider the case where R is a commutative ring with identity of odd prime characteristic and G is a nontrivial locally finite group. We show that in this case, if the units in RG are all trivial, then G must be cyclic of order two. These results improve on a result of Herman et al. 'Trivial units for group rings with G-adapted coefficient rings', Canad. Math. Bull. 48(1) (2005), 80-89].

Item Type: | Article |
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Funders: | None |

Uncontrolled Keywords: | Group ring; Unit; Torsion group; Locally finite group |

Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Science |

Depositing User: | Ms. Juhaida Abd Rahim |

Date Deposited: | 25 Apr 2022 06:20 |

Last Modified: | 25 Apr 2022 06:20 |

URI: | http://eprints.um.edu.my/id/eprint/33810 |

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