Unit Groups of group algebras of certain quasidihedral group

TL;DR

This paper determines the complete structure of unit groups in group algebras over finite fields for specific quasidihedral groups of orders 16 and 32, expanding understanding of algebraic structures in modular group algebras.

Contribution

It provides the first detailed descriptions of unit groups for group algebras of quasidihedral groups of orders 16 and 32 over finite fields.

Findings

Complete structure of unit groups for $F_q[QD_{16}]$ and $F_q[QD_{32}]$

Explicit algebraic descriptions of units in these group algebras

Extension of known results to specific quasidihedral groups

Abstract

Let $F_{q}$ be any finite field of characteristic $p>0$ having $q = p^{n}$ elements. In this paper, we have obtained the complete structure of unit groups of group algebras $F_{q}[QD_{2^k}]$, for $k = 4$ and $5$, for any prime $p>0$, where $QD_{2^k}$ is quasidihedral group of order $2^k$