Rudolf Maier

ON THE LOCAL HYPERCENTER OF A GROUP

We introduce a local hypercenter of an arbitrary group and study its basic properties. With this concept, it turns out that classical theorems of Baer, Mal’cev and McLain on locally nilpotent groups can be obtained as special cases of statements which are valid in any group. Furthermore, we investigate the connection between the local hypercenter of a group and the intersection of its maximal locally nilpotent subgroups.

A note on subnormality in factorizable finite groups

Let G be a finite group, X a subgroup of G, and oNo(x) = {ge GIX< < (X,X~)} be the subnormalizer of X in G. One of the important problems in the theory of subnormal subgroups is to determine conditions which guarantee the subnormality of X in the group generated by ~NG(X). A result of the first author [3] and H. Wielandt [5] describes such a condition for finite factorizable groups. More precisely, the following is proved in [5],

Hypercentrally embedded subgroups of polycyclic-by-finite groups

Abstract. A subgroup of a polycyclic-by-finite group is hypercentrally embedded if and only if its projections into the finite quotients have this property.

Detecting hypercentrality from small subgroups

Abstract We show that the nilpotency of the metacyclic subgroups of a hypercyclic group implies the hypercentrality of the whole group. We also construct a center-free metabelian group all of whose polycyclic subgroups are abelian.