Remarks on Proficient groups

Details Remarks on Proficient groups Remarks on Proficient groups

2009-05-03

arxiv.org/abs/0905.0256v1

Mathematics

Group Theory

Scientific paper

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

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