Original scientific paper

https://doi.org/10.3336/gm.44.1.09

Finite p-groups in which some subgroups are generated by elements of order p

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

Abstract

We prove that if a p-group G of exponent pe > p has no subgroup H such that |Ω1(H)| = pp and H/Ω1(H) is cyclic of order pe-1 ≥ p 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.

Keywords

p-groups of maximal class; regular and absolutely regular p-groups; metacyclic p-groups; Lp-groups

Hrčak ID:

36950

URI

https://hrcak.srce.hr/36950

Publication date:

21.5.2009.

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