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

Capability of Some 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 generalisation of a theorem of Baer for the small class case. The approach may also be used to obtain some recent results on the capability of certain nilpotent groups of class 2. We also obtain a necessary condition for the capability of an arbitrary p-grou...

Some Inequalities for Nilpotent Multipliers of Powerful p-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 ...

On the Nilpotent Multiplier of a Free Product

Capability of Nilpotent Products of Cyclic Groups Ii

In Part I it was shown that if G is a p-group of class k, generated by elements of orders 1 < p1 ≤ · · · ≤ pr , then a necessary condition for the capability of G is that r > 1 and αr ≤ αr−1 + ⌊ k−1 p−1 ⌋. It was also shown that when G is the k-nilpotent product of the cyclic groups generated by those elements and k = p = 2 or k < p, then the given conditions are also sufficient. We make a corr...

Some Remarks on Nilpotent Groups with Roots

is soluble for every pG.m and every gGG. Similarly we call a group G a Dor-group if the equation (1) (above) is not only soluble, but uniquely soluble. The class of Fur-groups and the class of Dor-groups will be denoted respectively by Em and Dm. Clearly Em~2)Dm. There is a less trivial relationship between these two classes of groups. If we denote by ©(C) the class of groups which occur as hom...