Determinant for automorphisms of semidirect product of groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912499864961024 |
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| author | Lal, Ratan Choudhary, Alka Kakkar, Vipul |
| author_facet | Lal, Ratan Choudhary, Alka Kakkar, Vipul |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18456 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Determinant for automorphisms of semidirect product of groups Lal, Ratan Choudhary, Alka Kakkar, Vipul Group Theory 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. |
| title | Determinant for automorphisms of semidirect product of groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2507.18456 |