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2017 New topological methods to solve equations over groups
Anton Klyachko, Andreas Thom
Algebr. Geom. Topol. 17(1): 331-353 (2017). DOI: 10.2140/agt.2017.17.331

Abstract

We show that the equation associated with a group word w G F2 can be solved over a hyperlinear group G if its content — that is, its augmentation in F2 — does not lie in the second term of the lower central series of F2. Moreover, if G is finite, then a solution can be found in a finite extension of G. The method of proof extends techniques developed by Gerstenhaber and Rothaus, and uses computations in p–local homotopy theory and cohomology of compact Lie groups.

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Anton Klyachko. Andreas Thom. "New topological methods to solve equations over groups." Algebr. Geom. Topol. 17 (1) 331 - 353, 2017. https://doi.org/10.2140/agt.2017.17.331

Information

Received: 8 December 2015; Revised: 23 March 2016; Accepted: 27 May 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06680250
MathSciNet: MR3604379
Digital Object Identifier: 10.2140/agt.2017.17.331

Subjects:
Primary: 20F70, 22C05

Rights: Copyright © 2017 Mathematical Sciences Publishers

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