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ON MAXIMAL CYCLIC SUBGROUPS OF FINITE GROUPS

Part of: Representation theory of groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  12 February 2026

RAIMUNDO BASTOS Open the ORCID record for RAIMUNDO BASTOS [Opens in a new window]  and
DEYFILA LIMA Open the ORCID record for DEYFILA LIMA [Opens in a new window]
RAIMUNDO BASTOS
Affiliation:
Departamento de Matemática, Universidade de Brasília , Brasília - DF, 70910-900, Brazil e-mail: bastos@mat.unb.br
DEYFILA LIMA*
Affiliation:
Departamento de Matemática, Universidade de Brasília , Brasília - DF, 70910-900, Brazil
*
e-mail: deyfilaa@gmail.com
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Abstract

Let $\lambda (G)$ be the maximum number of subgroups in an irredundant cover of the finite group G. We establish bounds on the order, exponent and derived length of the group in terms of this invariant.

Keywords

finite groupmaximal covermaximal cyclic subgroupflower groupn-centraliser groups solvabilityMCB family

MSC classification

Primary: 20D60: Arithmetic and combinatorial problems
Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20D15: Nilpotent groups, $p$-groups 20D25: Special subgroups (Frattini, Fitting, etc.) 20F16: Solvable groups, supersolvable groups

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 9
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Copyright
© The Author(s), 2026. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The first author acknowledges the support of CNPq (Project Nos. 303191/2022-8 and 200116/2025-8) and FAPDF. The second author was partially supported by CNPq (Project No. 140429/2025-5).

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