Open Access
Spring 2016 Embedding of groups and quadratic equations over groups
D. F. Cummins, S. V. Ivanov
Illinois J. Math. 60(1): 99-115 (Spring 2016). DOI: 10.1215/ijm/1498032025


We prove that, for every integer $n\ge2$, a finite or infinite countable group $G$ can be embedded into a 2-generated group $H$ in such a way that the solvability of quadratic equations of length at most $n$ is preserved, that is, every quadratic equation over $G$ of length at most $n$ has a solution in $G$ if and only if this equation, considered as an equation over $H$, has a solution in $H$.


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D. F. Cummins. S. V. Ivanov. "Embedding of groups and quadratic equations over groups." Illinois J. Math. 60 (1) 99 - 115, Spring 2016.


Received: 30 August 2015; Revised: 19 July 2016; Published: Spring 2016
First available in Project Euclid: 21 June 2017

zbMATH: 1372.20032
MathSciNet: MR3665173
Digital Object Identifier: 10.1215/ijm/1498032025

Primary: 20F05 , 20F06 , 20F70

Rights: Copyright © 2016 University of Illinois at Urbana-Champaign

Vol.60 • No. 1 • Spring 2016
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