Original scientific paper

https://doi.org/10.3336/gm.46.1.10

The number of subgroups of given order in a metacyclic p-group

Yakov Berkovich ; Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel

Abstract

This note was inspired by A. Mann's letter [3] at June 28, 2009, in which the number of subgroups of given order in a metacyclic p-group for odd primes p was computed. Below we present another proof of that result. The offered proof is extended to so called quasi-regular metacyclic 2-groups. In Sec. 2 we compute the number of cyclic subgroups of given order in metacyclic 2-groups. In Sec. 3 we complete computation of the number of subgroups of given order in metacyclic 2-groups. In Sec. 4 we study the metacyclic p-groups with small minimal nonabelian subgroups or sections.

Keywords

Metacyclic p-groups; quasi-regular metacyclic p-groups; section, Hall's enumeration principle

Hrčak ID:

68882

URI

https://hrcak.srce.hr/68882

Publication date:

13.6.2011.

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