A Note on Lagrange Subsets of Finite Groups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912791948951552 |
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| author | Kabenyuk, Mikhail |
| author_facet | Kabenyuk, Mikhail |
| contents | In a finite group, a subset is called a Lagrange subset if its size divides the group order, and a factor if it admits a complementary subset. We provide a new and comparatively direct proof of the classification of groups in which every Lagrange subset is a factor. We show that any nontrivial such group must be a cyclic group of prime order, the cyclic group of order 4, or an elementary abelian group of order 4, 8, or 9. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Note on Lagrange Subsets of Finite Groups Kabenyuk, Mikhail Group Theory 20D60 In a finite group, a subset is called a Lagrange subset if its size divides the group order, and a factor if it admits a complementary subset. We provide a new and comparatively direct proof of the classification of groups in which every Lagrange subset is a factor. We show that any nontrivial such group must be a cyclic group of prime order, the cyclic group of order 4, or an elementary abelian group of order 4, 8, or 9. |
| title | A Note on Lagrange Subsets of Finite Groups |
| topic | Group Theory 20D60 |
| url | https://arxiv.org/abs/2512.22900 |