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 $A_qA_r$.
A$ 群的一些特殊品种中的群枚举
我们发现了在 $G = A_pA_qA_r$(其中 $p$、$q$ 和 $r$ 是不同的素数)中阶数 $n$ 直至同构的群的数量上限。我们还发现了一个关于阶数和子群共轭类数的约束,这些子群在同在 $A_qA_r$ 中的泛线性群的子群中是最大的。
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