On the capability of finite groups of class two and prime exponent

Details On the capability of finite groups of class two and prime exponent On the capability of finite groups of class two and prime exponent

2007-08-17

arxiv.org/abs/0708.2391v2

Mathematics

Group Theory

43 pp; incorporates results from older paper; fix amsrefs/hyperref incompatibility and a typo

Scientific paper

We consider the capability of $p$-groups of class two and odd prime exponent. The question of capability is shown to be equivalent to a statement about vector spaces and linear transformations, and using the equivalence we give proofs of some old results and several new ones. In particular, we establish a number of new necessary and new sufficient conditions for capability, including a sufficient condition based only on the ranks of $G/Z(G)$ and $[G,G]$. Finally, we characterise the capable groups among the 5-generated groups in this class.

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