Finite p-groups in which the normal closure of each non-normal cyclic subgroup is nonabelian - Janko, Zvonimir (Glasnik matematički, 2014)
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.
Gesehen am 22.02.2018