Glasnik Matematicki, Vol. 49, No. 2 (2014), 333-336.
FINITE P-GROUPS IN WHICH THE NORMAL CLOSURE OF EACH NON-NORMAL CYCLIC SUBGROUP IS NONABELIAN
Mathematical Institute, University of Heidelberg,
69120 Heidelberg, Germany
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.
2010 Mathematics Subject Classification.
Key words and phrases. Finite p-groups, normal closure, quasidihedral 2-groups, quasi-generalized quaternion groups, exponent of a p-group.
Full text (PDF) (access from subscribing institutions only)
- Y. Berkovich, Groups of prime power order, Vol. 1, Walter de Gruyter, Berlin-New York, 2008.
- Y. Berkovich and Z. Janko, Groups of prime power order, Vol. 3, Walter de Gruyter, Berlin-New York, 2011.
- Y. Berkovich and Z. Janko, Groups of prime power order, Vol. 5, Walter de Gruyter, Berlin-New York, 2014.
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