## Abstract

Let KG denote the group algebra of the group G over the field K

and let U(KG) denote its group of units. Here without the use of a computer we

give presentations for the unit groups of all group algebras KG, where the size of

KG is less than 1024. As a consequence we find the minimum counterexample

to the Isomorphism Problem for group algebras.

and let U(KG) denote its group of units. Here without the use of a computer we

give presentations for the unit groups of all group algebras KG, where the size of

KG is less than 1024. As a consequence we find the minimum counterexample

to the Isomorphism Problem for group algebras.

Original language | English (Ireland) |
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Pages (from-to) | 531-537 |

Journal | International Journal of Pure and Applied Mathematics |

Volume | 49 |

Issue number | 4 |

Publication status | Published - 2008 |

## Keywords

- group ring
- group algebra
- unit group
- isomorphism problem

## Name of Affiliated ATU Research Unit

- MISHE - Mathematical Modelling and Intelligent Systems for Health & Environment