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

Arturo Magidin

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

Group Theory 2007-05-23 v1

Authors: Arturo Magidin

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.

Keywords

capable groups p-groups central factor groups class of groups minimal generators order of elements

Cite

@article{arxiv.math/0405087,
  title  = {On the orders of generators of capable $p$-groups},
  author = {Arturo Magidin},
  journal= {arXiv preprint arXiv:math/0405087},
  year   = {2007}
}

Comments

4 pp

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