Integer group determinants for ${\rm C}_{2}^{4}$

TL;DR

This paper completely characterizes the set of all possible integer group determinants for the group ${ m C}_{2}^{4}$, providing a comprehensive understanding of its algebraic structure.

Contribution

It explicitly determines all possible integer group determinants for ${ m C}_{2}^{4}$, a previously unresolved problem in algebraic combinatorics.

Findings

All possible integer group determinants for ${ m C}_{2}^{4}$ are identified.

The structure of the determinant values is fully characterized.

Results extend understanding of group determinants for elementary abelian 2-groups.

Abstract

We determine all possible values of the integer group determinant of ${\rm C}_{2}^{4}$, where ${\rm C}_{2}$ is the cyclic group of order $2$.