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

Arturo Magidin

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

Arturo Magidin

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Abstract

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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Arturo Magidin. 2004-05-05. On the orders of generators of capable $p$-groups. https://arxiv.org/abs/math/0405087

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