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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.08586 |
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| _version_ | 1866917775139667968 |
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| author | Arushi Venkataraman, Geetha |
| author_facet | Arushi Venkataraman, Geetha |
| contents | We find an upper bound for the number of groups of order $n$ up to isomorphism in the variety $G = A_pA_qA_r$, where $p$, $q$ and $r$ are distinct primes. We also find a bound on the orders and on the number of conjugacy classes of subgroups that are maximal amongst the subgroups of the general linear group that are also in the variety $A_qA_r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08586 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enumeration of groups in some special varieties of $A$-groups Arushi Venkataraman, Geetha Group Theory 20B15, 20B35, 20D10, 20E10, 20E45, 20H30. 20B15, 20B35, 20D10, 20E10, 20E45, 20H30 We find an upper bound for the number of groups of order $n$ up to isomorphism in the variety $G = A_pA_qA_r$, where $p$, $q$ and $r$ are distinct primes. We also find a bound on the orders and on the number of conjugacy classes of subgroups that are maximal amongst the subgroups of the general linear group that are also in the variety $A_qA_r$. |
| title | Enumeration of groups in some special varieties of $A$-groups |
| topic | Group Theory 20B15, 20B35, 20D10, 20E10, 20E45, 20H30. 20B15, 20B35, 20D10, 20E10, 20E45, 20H30 |
| url | https://arxiv.org/abs/2409.08586 |