Capability of Nilpotent Products of Cyclic Groups
نویسنده
چکیده
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 class k, and some further results.
منابع مشابه
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...
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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...
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