CONJUGACY CLASSES OF MAXIMAL CYCLIC SUBGROUPS AND NILPOTENCE CLASS OF -GROUPS

Mariagrazia Bianchi; Rachel D. Camina; Mark L. Lewis

doi:10.17863/cam.83473

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CONJUGACY CLASSES OF MAXIMAL CYCLIC SUBGROUPS AND NILPOTENCE CLASS OF -GROUPS

Mariagrazia Bianchi Rachel D. Camina Mark L. Lewis

Year: 2022 Journal: Bulletin of the Australian Mathematical Society Vol: 106 (3)Pages: 463-469 Publisher: Cambridge University Press

DOI: 10.17863/cam.83473

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Abstract

Abstract Let $\eta (G)$ be the number of conjugacy classes of maximal cyclic subgroups of G . We prove that if G is a p -group of order $p^n$ and nilpotence class l , then $\eta (G)$ is bounded below by a linear function in $n/l$ .

Keywords:

Conjugacy class Mathematics Order (exchange) Class (philosophy) Bounded function Combinatorics Pure mathematics Cyclic group Mathematical analysis

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Finite Group Theory Research

Physical Sciences → Mathematics → Discrete Mathematics and Combinatorics

Coding theory and cryptography

Physical Sciences → Computer Science → Artificial Intelligence

Limits and Structures in Graph Theory

Physical Sciences → Mathematics → Discrete Mathematics and Combinatorics

CONJUGACY CLASSES OF MAXIMAL CYCLIC SUBGROUPS AND NILPOTENCE CLASS OF -GROUPS

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