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

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.

19 pages, 4 tables, 0 figures