Embedding groups of class two and prime exponent in capable and non-capable groups

Details Embedding groups of class two and prime exponent in capable and non-capable groups Embedding groups of class two and prime exponent in capable and non-capable groups

2008-05-26

arxiv.org/abs/0805.4000v3

Bull. Austral. Math. Soc. 79 (2009), 303-308

Mathematics

Group Theory

5 pages; title change, minor corrections

Scientific paper

We show that if $G$ is any $p$-group of class at most two and exponent $p$,
then there exist groups $G_1$ and $G_2$ of class two and exponent $p$ that
contain $G$, neither of which can be expressed as a central product, and with
$G_1$ capable and $G_2$ not capable. We provide upper bounds for ${\rm
rank}(G_i^{\rm ab})$ in terms of ${\rm rank}(G^{\rm ab})$ in each case.

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