On the structure of generalized Hamiltonian groups

We consider the characteristic subgroup CS(G), generated by the nonnormal c yclic subgroups of the group G. A group G is called a generalized Dedekind group if CS(G)I G, and those among them with nontrivial CS(G) are called ge neralized Hamiltonian groups. Such groups are torsion groups of nilpotency class two. The commutator subgroup is cyclic of p-power or two times p-powe r order and always contained in CS(G). The quotient G/CS(G) is a locally cy clic p-group. We give an example of an infinite generalized Hamiltonian p-g roup with G/CS(G) locally cyclic.