Glasnik Matematicki, Vol. 41, No.2 (2006), 259-269.

ON THE METACYCLIC EPIMORPHIC IMAGES OF FINITE p-GROUPS

Yakov Berkovich

Abstract.   We prove that if G is a p-group of order p^m > pⁿ, where n > 3 for p = 2 and n > 2 for p > 2, then the number of normal subgroups D of G such that G/D is metacyclic of order pⁿ is a multiple of p, unless G is metacyclic. We also give a very short and elementary proof of the following result: representation groups of nonabelian metacyclic p-groups are metacyclic.

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   Finite p-groups, metacyclic p-groups, minimal nonabelian p-groups, Schur multiplier, representation group.

DOI: 10.3336/gm.41.2.08

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