Glasnik Matematicki, Vol. 44, No.1 (2009), 167-175.

FINITE p-GROUPS IN WHICH SOME SUBGROUPS ARE GENERATED BY ELEMENTS OF ORDER p

Yakov Berkovich

Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel


Abstract.   We prove that if a p-group G of exponent pe > p has no subgroup H such that 1(H)| = pp and H1(H) is cyclic of order pe-1p and H is regular provided e = 2, then G is either absolutely regular or of maximal class. This result supplements the fundamental theorem of Blackburn on p-groups without normal subgroups of order pp and exponent p. For p > 2, we deduce even stronger result than (respective result for p = 2 is unknown) a theorem of Bozikov and Janko.

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   p-groups of maximal class, regular and absolutely regular p-groups, metacyclic p-groups, Lp-groups.


Full text (PDF) (free access)

DOI: 10.3336/gm.44.1.09


References:

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