Non-existence of partial difference sets of order 8p^3 in Abelian groups

TL;DR

This paper proves that nontrivial partial difference sets do not exist in Abelian groups of order 8p^3 for primes p ≥ 3, clarifying the structure of such combinatorial objects.

Contribution

It establishes the non-existence of certain partial difference sets in specific Abelian groups, extending understanding of their algebraic and combinatorial properties.

Findings

No nontrivial partial difference sets in Abelian groups of order 8p^3 for p ≥ 3

Provides a classification constraint for difference sets in algebraic structures

Enhances knowledge of combinatorial design limitations in group theory

Abstract

In this paper we prove non-existence of nontrivial partial difference sets in Abelian groups of order 8p^3, where p \geq 3 is a prime number.