Remarks on Proficient groups
Group Theory
2009-05-05 v1
Abstract
If a finite group G has a presentation with d generators and r relations, it is well-known that r - d is at least the rank of the Schur multiplier of G; a presentation is called efficient if equality holds. There is an analogous definition for proficient profinite presentations. We show that many perfect groups have proficient presentations. Moreover, we prove that infinitely many alternating groups, symmetric groups and their double covers have proficient presentations
Cite
@article{arxiv.0905.0256,
title = {Remarks on Proficient groups},
author = {R. M. Guralnick and W. M. Kantor and M. Kassabov and A. Lubotzky},
journal= {arXiv preprint arXiv:0905.0256},
year = {2009}
}