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arXiv · 2507.18456

Determinant for automorphisms of semidirect product of groups

Ratan Lal·Alka Choudhary·Vipul Kakkar
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Abstract

A description of the endomorphisms of semidirect products of two groups as a group of $2\times 2$ 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.

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Ratan Lal, Alka Choudhary, Vipul Kakkar. 2025-07-24. Determinant for automorphisms of semidirect product of groups. https://arxiv.org/abs/2507.18456

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