Unit group of $\f_{p^k}\SL(3,2),p\geq 11$

TL;DR

This paper determines the structure of the unit group of the algebra formed by the group algebra of SL(3,2) over finite fields with prime power order, for primes p ≥ 11.

Contribution

It explicitly describes the unit group structure of the algebra _{p^k}(SL(3,2)), a novel result in algebraic group theory and finite field applications.

Findings

Explicit structure of the unit group provided

Results applicable for all primes p  11

Advances understanding of algebraic groups over finite fields

Abstract

We provide the structure of the unit group of $\f_{p^k}(\SL(3,2))$, where $p\geq 11$ is a prime and $\SL(3,2)$ denotes the $3\times 3$ invertible matrices over $\f_2$.