Unitary Units of The Group Algebra ${\mathbb{F}}_{2^k}Q_{8}$

TL;DR

This paper characterizes the structure of the unitary units within the group algebra over a finite field, revealing it as a Hamiltonian group, which advances understanding of algebraic structures in finite fields.

Contribution

It provides a detailed description of the unitary unit group of the group algebra ${}_{2^k} Q_{8}$ as a Hamiltonian group, a novel structural insight.

Findings

The unitary unit group is a Hamiltonian group.

Explicit structure of the unitary units in ${}_{2^k} Q_{8}$.

Enhanced understanding of algebraic properties of group algebras over finite fields.

Abstract

The structure of the unitary unit group of the group algebra ${\F}_{2^k} Q_{8}$ is described as a Hamiltonian group.