Enumeration of groups in some special varieties of $A$-groups

Arushi; Geetha Venkataraman

doi:10.1017/s0004972724000431

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arXiv · 2409.08586

Enumeration of groups in some special varieties of $A$-groups

Arushi·Geetha Venkataraman

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Abstract

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 $A_qA_r$.

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Arushi, Geetha Venkataraman. 2024-09-13. Enumeration of groups in some special varieties of $A$-groups. https://doi.org/10.1017/s0004972724000431

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