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ENUMERATION OF GROUPS IN SOME SPECIAL VARIETIES OF A-GROUPS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 111 / Issue 1 / February 2025
- Published online by Cambridge University Press:
- 27 August 2024, pp. 107-117
- Print publication:
- February 2025
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- Article
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We find an upper bound for the number of groups of order n up to isomorphism in the variety
${\mathfrak {S}}={\mathfrak {A}_p}{\mathfrak {A}_q}{\mathfrak {A}_r}$, 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 
$\mathfrak {A}_q\mathfrak {A}_r$.
