Remarks on proficient groups

R. M. Guralnick; W. M. Kantor; M. Kassabov; A. Lubotzky

doi:10.1016/j.jalgebra.2009.05.018

Remarks on proficient groups

R. M. Guralnick, W. M. Kantor, M. Kassabov, A. Lubotzky

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	169-184
Number of pages	16
Journal	Journal of Algebra
Volume	326
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2009.05.018
State	Published - 15 Jan 2011

Keywords

Cohomology
Efficient groups
Presentations of finite groups
Proficient groups
Profinite groups

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jalgebra.2009.05.018

Cite this

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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.",

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KW - Cohomology

KW - Efficient groups

KW - Presentations of finite groups

KW - Proficient groups

KW - Profinite groups

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DO - 10.1016/j.jalgebra.2009.05.018

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JO - Journal of Algebra

JF - Journal of Algebra

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ER -

Remarks on proficient groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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