A Characterization of Group Through Isomorphism Classes of Transversals
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916082768412672 |
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| author | Jain, Vivek Kumar Rawat, Raja |
| author_facet | Jain, Vivek Kumar Rawat, Raja |
| contents | Let G be a group and H a subgroup of G of finite index. In this article, it is proved that if the number of isomorphism classes of right transversals of H in G is 5, then the index of H in G is 6 and the permutation representation of G on right cosets of H in G is isomorphic to the alternating group on four symbols. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13363 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Characterization of Group Through Isomorphism Classes of Transversals Jain, Vivek Kumar Rawat, Raja Group Theory 20D60, 20N05 Let G be a group and H a subgroup of G of finite index. In this article, it is proved that if the number of isomorphism classes of right transversals of H in G is 5, then the index of H in G is 6 and the permutation representation of G on right cosets of H in G is isomorphic to the alternating group on four symbols. |
| title | A Characterization of Group Through Isomorphism Classes of Transversals |
| topic | Group Theory 20D60, 20N05 |
| url | https://arxiv.org/abs/2306.13363 |