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ENUMERATION OF GROUPS IN SOME SPECIAL VARIETIES OF A-GROUPS

Part of: Structure and classification of infinite or finite groups Representation theory of groups Other groups of matrices Permutation groups

Published online by Cambridge University Press:  27 August 2024

ARUSHI Open the ORCID record for ARUSHI [Opens in a new window]  and
GEETHA VENKATARAMAN Open the ORCID record for GEETHA VENKATARAMAN [Opens in a new window]
ARUSHI
Affiliation:
School of Liberal Studies (Mathematics), Dr. B. R. Ambedkar University Delhi, Delhi 110006, India e-mail: arushi.18@stu.aud.ac.in, arushi.garvita@gmail.com
GEETHA VENKATARAMAN*
Affiliation:
School of Liberal Studies (Mathematics), Dr. B. R. Ambedkar University Delhi, Delhi 110006, India
*
e-mail: geetha@aud.ac.in, geevenkat@gmail.com
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Abstract

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 $\mathfrak {A}_q\mathfrak {A}_r$.

Keywords

group enumerationvariety of groupsgeneral linear groupsymmetric grouptransitive subgroupprimitive subgroupconjugacy class

MSC classification

Primary: 20E10: Quasivarieties and varieties of groups
Secondary: 20B15: Primitive groups 20B35: Subgroups of symmetric groups 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20E45: Conjugacy classes 20H30: Other matrix groups over finite fields
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 111 , Issue 1 , February 2025 , pp. 107 - 117
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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