Difference sets disjoint from a subgroup II: groups of order $4p^2$

Stephen P. Humphries; Nathan L. Nicholson

Difference sets disjoint from a subgroup II: groups of order $4p^2$

Group Theory 2021-03-19 v1 Combinatorics

Authors: Stephen P. Humphries , Nathan L. Nicholson

Abstract

We study finite groups $G$ having a normal subgroup $H$ and $D \subset G \setminus H, D \cap D^{-1}=\emptyset,$ such that the multiset $\{ xy^{-1}:x,y \in D\}$ has every non-identity element occur the same number of times (such a $D$ is called a {\it DRAD difference set}). We show that there are no such groups of order $4p^2$ , where $p$ is an odd prime.

Keywords

finite groups finite group theory

Cite

@article{arxiv.2103.09892,
  title  = {Difference sets disjoint from a subgroup II: groups of order $4p^2$},
  author = {Stephen P. Humphries and Nathan L. Nicholson},
  journal= {arXiv preprint arXiv:2103.09892},
  year   = {2021}
}

Comments

15 pages

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