Another article on the number of homomorphisms
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918422513713152 |
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| author | Khudyakov, Alexander V. |
| author_facet | Khudyakov, Alexander V. |
| contents | We extend the class of abelian groups for which a conjecture of Asai and Yoshida on the number of crossed homomorphisms holds. We also prove a general result which connects certain problems concerning divisibility in groups to the Asai-Yoshida conjecture. One of the consequences is that for finite groups F and G the number |Hom(F,G)| is divisible by gcd(|G|, |F:F'|) if F/F' is a product of a cyclic group and a group with cube-free exponent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16552 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Another article on the number of homomorphisms Khudyakov, Alexander V. Group Theory We extend the class of abelian groups for which a conjecture of Asai and Yoshida on the number of crossed homomorphisms holds. We also prove a general result which connects certain problems concerning divisibility in groups to the Asai-Yoshida conjecture. One of the consequences is that for finite groups F and G the number |Hom(F,G)| is divisible by gcd(|G|, |F:F'|) if F/F' is a product of a cyclic group and a group with cube-free exponent. |
| title | Another article on the number of homomorphisms |
| topic | Group Theory |
| url | https://arxiv.org/abs/2511.16552 |