Glasnik matematički, Vol. 46 No. 1, 2011.
Izvorni znanstveni članak
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
Sažetak
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.
Ključne riječi
Metacyclic p-groups; quasi-regular metacyclic p-groups; section, Hall's enumeration principle
Hrčak ID:
68882
URI
Datum izdavanja:
13.6.2011.
Posjeta: 1.022 *