Solvable quotients of subdirect products of perfect groups are nilpotent

Keith Kearnes; Peter Mayr; Nik Ruskuc

doi:10.1112/blms.12196

Solvable quotients of subdirect products of perfect groups are nilpotent

Keith Kearnes, Peter Mayr, Nik Ruskuc

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Abstract

We prove the statement in the title and exhibit examples of quotients of arbitrary nilpotency class. This answers a question by Holt.

Original language	English
Pages (from-to)	1016-1026
Number of pages	11
Journal	Bulletin of the London Mathematical Society
Volume	50
Issue number	6
Early online date	9 Aug 2018
DOIs	https://doi.org/10.1112/blms.12196
Publication status	Published - Dec 2018

Keywords

Subdirect product
Subgroup
Perfect group
Nilpotent

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10.1112/blms.12196

Perfect10
© 2018 London Mathematical Society. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at: https://doi.org/10.1112/blms.12196
Accepted author manuscript, 279 KB

Nik Ruskuc
- nik.ruskucst-andrews.acuk
- Pure Mathematics - Professor
- Centre for Interdisciplinary Research in Computational Algebra
Person: Academic

Cite this

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title = "Solvable quotients of subdirect products of perfect groups are nilpotent",

abstract = "We prove the statement in the title and exhibit examples of quotients of arbitrary nilpotency class. This answers a question by Holt.",

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KW - Subdirect product

KW - Subgroup

KW - Perfect group

KW - Nilpotent

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JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

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Solvable quotients of subdirect products of perfect groups are nilpotent

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Nik Ruskuc

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