English

Determinant for automorphisms of semidirect product of groups

Group Theory 2025-07-25 v1

Abstract

A description of the endomorphisms of semidirect products of two groups as a group of 2×22\times 2 matrices of maps is already known. Using this description, we have studied the concept of determinant for the endomorphisms of semidirect product of two groups. A characterization of the invertible endomorphisms is given with the help of the tools developed using the determinants.

Keywords

Cite

@article{arxiv.2507.18456,
  title  = {Determinant for automorphisms of semidirect product of groups},
  author = {Ratan Lal and Alka Choudhary and Vipul Kakkar},
  journal= {arXiv preprint arXiv:2507.18456},
  year   = {2025}
}

Comments

This is a first draft. Comments welcome