## Abstract

Let FG be the group algebra of a finite p-group G over a finite field F of positive characteristic p. Let be an involution of the algebra FG which is a linear extension of an anti-automorphism of the group G to FG. If p is an odd prime, then the order of the -unitary subgroup of FG is established. For the case p = 2, we generalize a result obtained for finite abelian 2-groups. It is proved that the order of the ∗-unitary subgroup of FG of a non-abelian 2-group is always divisible by a number which depends only on the size of F, the order of G and the number of elements of order two in G. Moreover, we show that the order of the ∗-unitary subgroup of FG determines the order of the finite p-group G.

Original language | English |
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Pages (from-to) | 1327-1334 |

Number of pages | 8 |

Journal | International Journal of Algebra and Computation |

Volume | 32 |

Issue number | 7 |

DOIs | |

Publication status | Published - Nov 1 2022 |

## Keywords

- Group algebras
- unit group of group algebras
- unitary subgroups

## ASJC Scopus subject areas

- Mathematics(all)