On the orders of generators of capable p-groups

2004/05/05 by Arturo Magidin
Mathematics · #math.GR #msc:20D15

paper · pdf

published as Bull. Austral. Math. Soc. 70 no. 3, 391-395 (2004) · 4 pp

arxiv created 2004/05/05 · arxiv updated 2009/12/01

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(c-1)/(p-1)\rfloor}. This is best possible.

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