Automorphisms of Zappa-Sz\'{e}p Product

TL;DR

This paper determines the automorphism groups of Zappa-Szép products of groups, including specific cases involving cyclic groups of prime power order, advancing understanding of their symmetries.

Contribution

It explicitly computes automorphism groups for Zappa-Szép products, including a new case involving cyclic groups of order m and p^2.

Findings

Automorphism group of Zappa-Szép product of two groups identified.

Automorphism group of cyclic groups of order m and p^2 computed.

Provides explicit automorphism groups for specific Zappa-Szép products.

Abstract

In this paper, we have found the automorphism group of the Zappa-Sz\'{e}p product of two groups. Also, we have computed the automorphism group of the Zappa-Sz\'{e}p product of a cyclic group of order $m$ and a cyclic group of order $p^{2}$, where $p$ is a prime.