TY - JOUR

T1 - Embedding of groups and quadratic equations over groups

AU - Cummins, D. F.

AU - Ivanov, S. V.

N1 - Funding Information:
The second author was supported in part by the NSF under grant DMS 09-01782. 2010 Mathematics Subject Classification. 20F05, 20F06, 20F70.
Publisher Copyright:
© 2017 University of Illinois.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2016

Y1 - 2016

N2 - We prove that, for every integer n ≥ 2, 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.

AB - We prove that, for every integer n ≥ 2, 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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U2 - 10.1215/ijm/1498032025

DO - 10.1215/ijm/1498032025

M3 - Article

VL - 60

SP - 99

EP - 115

JO - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

SN - 0019-2082

IS - 1

ER -