Year: 2025
Type: preprint
Abstract: We show that the integer group determinants for the general affine group of degree one, $GA(1,q)$ with $q=p^k$ a prime power, take the form $D=AB^{q-1},$ where $A$ is a $\mathbb Z_{q-1}$ integer group determinant and $B\equiv A \bmod q$. This generalizes the result for $k=1$. When $2^k-1$ is a Mersenne prime we show that this condition is both necessary and sufficient for $GA(1,2^k).$ The same is true for $GA(1,9)$ and $GA(1,27)$, but interestingly not for $GA(1,16)$.
Source: arXiv (Cornell University)
Authors: Ostergaard, Andrew, Pinner, Chris
Institutions: University of Southern Indiana, Kansas State University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6947913744
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