Hypersubtraction and semi-direct product

TL;DR

This paper introduces an extrinsic approach to semi-direct products in group theory, utilizing hypersubtraction and hyper-Slominski structures to characterize this concept externally, complementing existing intrinsic methods.

Contribution

It presents a novel extrinsic framework for semi-direct products in groups using hypersubtraction and hyper-Slominski structures, expanding the understanding of group decompositions.

Findings

Extrinsic approach to semi-direct products developed

Hypersubtraction and hyper-Slominski structures characterized

Provides new tools for group decomposition analysis

Abstract

In this article, we introduce an extrinsic approach to the notion of semi-direct product, an intrinsic one (namely inside the category Gp of group itself) having been already done elsewhere. This will led us to focus our attention on two algebraic structures (hypersubtraction and hyper-Slominski settings) which will allow us to characterize this extrinsic explicitation.