The Product of a Semi Dihedral Group And a Cyclic Group

TL;DR

This paper characterizes the structure of a group formed by the product of a semi dihedral group and a cyclic group, where their intersection is trivial.

Contribution

It provides a detailed characterization of the group structure resulting from the product of a semi dihedral group and a cyclic group with trivial intersection.

Findings

Explicit description of the group structure $X(G)$

Conditions under which the product forms a specific group type

Insights into the interaction between semi dihedral and cyclic groups

Abstract

Let $X(G)=GC$ be a group, where $G$ is a semi dihedral group and $C$ is a cyclic group such that $G\cap C=1$. In this paper, $X(G)$ will be characterized.