Capability of certain nilpotent products of cyclic groups

Details Capability of certain nilpotent products of cyclic groups Capability of certain nilpotent products of cyclic groups

2003-07-25

arxiv.org/abs/math/0307345v3

Mathematics

Group Theory

Minor revision from version 2; some references corrected, a few more results given. 38 pp

Scientific paper

A group is called capable if it is a central factor group. We consider the capability of certain 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 $p$-group of class $k$, and some further results.

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