Capability of Some Nilpotent Products of Cyclic Groups

Capability of Nilpotent Products of Cyclic Groups

A group is called capable if it is a central factor group. We consider the capability of nilpotent products of cyclic groups, and obtain a generalization of a theorem of Baer for the small class case. The approach is also used to obtain some recent results on the capability of certain nilpotent groups of class 2. We also prove a necessary condition for the capability of an arbitrary p-group of ...

(c,1,...,1) Polynilpotent Multiplier of some Nilpotent Products of Groups

In this paper we determine the structure of (c,1,...,1) polynilpotent multiplier of certain class of groups. The method is based on the characterizing an explicit structure for the Baer invariant of a free nilpotent group with respect to the variety of polynilpotent groups of class row (c,1,...,1).

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups

On the Exponent of Triple Tensor Product of p-Groups

The non-abelian tensor product of groups which has its origins in algebraic K-theory as well as inhomotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, com...

On Semiabelian Groups

Recall that a group is called semiabelian if it is generated by its normal cyclic subgroups [6]. The class of semiabelian groups is a very natural generalization of the wellknown class of Dedekind groups (the groups in which all cyclic subgroups are normal). In the paper [6] Venzke showed that these groups could play a major role in the theory of supersoluble finite groups. Based on the notion ...