Original scientific paper

https://doi.org/10.3336/gm.49.2.07

Finite p-groups in which the normal closure of each non-normal cyclic subgroup is nonabelian

Zvonimir Janko ; Mathematical Institute, University of Heidelberg, 69120 Heidelberg, Germany

Abstract

We determine up to isomorphism finite non-Dedekindian p-groups G (i.e., p-groups which possess non-normal subgroups) such that the normal closure of each non-normal cyclic subgroup in G is nonabelian. It turns out that we must have p=2 and G has an abelian maximal subgroup A of exponent 2e, e≥ 3, and an element v G-A such that for all h A we have either hv=h-1 or hv=h -1+2e-1.

Keywords

Finite p-groups; normal closure; quasidihedral 2-groups; quasi-generalized quaternion groups; exponent of a p-group

Hrčak ID:

130887

URI

https://hrcak.srce.hr/130887

Publication date:

18.12.2014.

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