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Lower Bounds on the Number of Cyclic Subgroups in Finite Non-Cyclic Nilpotent Groups

Lower Bounds on the Number of Cyclic Subgroups in Finite Non-Cyclic Nilpotent Groups

Year:    2023

Author:    Wei Meng, Jiakuan Lu

Journal of Mathematical Study, Vol. 56 (2023), Iss. 1 : pp. 93–102

Abstract

Let G be a finite group and c(G) denote the number of cyclic subgroups of G. It is known that the minimal value of c on the set of groups of order n, where n is a positive integer, will occur at the cyclic group Zn. In this paper, for non-cyclic nilpotent groups G of order n, the lower bounds of c(G) are established.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v56n1.23.03

Journal of Mathematical Study, Vol. 56 (2023), Iss. 1 : pp. 93–102

Published online:    2023-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    p-groups cyclic subgroups Nilpotent groups.

Author Details

Wei Meng Email

Jiakuan Lu Email