On central difference sets in Suzuki $p$-groups of type $A$

TL;DR

This paper investigates the existence and construction of central difference sets in Suzuki p-groups of type A, providing non-existence results for even order and explicit constructions for odd order cases.

Contribution

It establishes non-existence results for certain central difference sets and constructs new examples in Suzuki p-groups, expanding understanding of their combinatorial structures.

Findings

No central difference sets when the order of θ is even.

Constructed central difference sets for odd order θ in A_2(m,θ).

Produced Latin square type partial difference sets for p>2.

Abstract

In this paper, when the order of $\theta$ is even, we prove that there exists no central difference sets in $A_2(m,\theta)$ and establish some non-existence results of central partial difference sets in $A_p(m,\theta)$ with $p>2$. When the order of $\theta$ is odd, we construct central difference sets in $A_2(m,\theta)$. Furthermore, we give some reduced linking systems of difference sets in $A_2(m,\theta)$ by using the difference sets we constructed. In the case $p>2$, we construct Latin square type central partial difference sets in $A_p(m,\theta)$ by a similar method.