Capable groups of prime exponent and class two

Details Capable groups of prime exponent and class two Capable groups of prime exponent and class two

2004-01-29

arxiv.org/abs/math/0401423v1

Mathematics

Group Theory

20 pp

Scientific paper

A group is called capable if it is a central factor group. We consider the capability of finite groups of class two and exponent $p$, $p$ an odd prime. We restate the problem of capability as a problem about linear transformations, which may be checked explicitly for any specific instance of the problem. We use this restatement to derive some known results, and prove new ones. Among them, we reduce the general problem to an oft-considered special case, and prove that a 3-generated group of class 2 and exponent $p$ is either cyclic or capable.

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