منابع مشابه
Factorization of »-soluble and »-nilpotent Groups
then we term the elements x and y n-commutative. It is not difficult to verify that »-commutativity and (1—»)-commutativity are equivalent properties of the elements x and y, that ( — ̂ -commutativity implies ordinary commutativity, and that commuting elements are »-commutative. From any concept and property involving the fact that certain elements [or functions of elements] commute, one may der...
متن کاملCapability 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 ...
متن کامل(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).
متن کاملCapability 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...
متن کاملCapability 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...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1986
ISSN: 0021-8693
DOI: 10.1016/0021-8693(86)90021-9