On the orders of generators of capable $p$-groups

Details On the orders of generators of capable $p$-groups On the orders of generators of capable $p$-groups

2004-05-05

arxiv.org/abs/math/0405087v1

Bull. Austral. Math. Soc. 70 no. 3, 391-395 (2004)

Mathematics

Group Theory

4 pp

Scientific paper

A group is called capable if it is a central factor group. For each prime $p$
and positive integer $c$, we prove the existence of a capable $p$-group of
class $c$ minimally generated by an element of order $p$ and an element of
order $p^{1+\lfloor\frac{c-1}{p-1}\rfloor}$. This is best possible.

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