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Exponential Genus Problems in one-relator products of groups

2005/06/03 by Andrew J. Duncan, Duncan, Andrew J.
Computer Science · Engineering · Mathematics · #20F05 #20F10 (Primary) 20F06 #20F65 #57M07 (Secondary) #Advanced Research in Systems and Signal Processing #FOS: Mathematics #Group Theory (math.GR) #Material Science and Thermodynamics #Mathematical Control Systems and Analysis #math.GR #msc:20F05 #msc:20F06 #msc:20F10 #msc:20F65 #msc:57M07

paper · pdf · doi:10.48550/arxiv.math/0506074

140 pages, 94 figures

arxiv created 2005/06/03 · openalex publication_date 2005/06/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Exponential equations in free groups were studied initially by Lyndon and Schutzenberger and then by Comerford and Edmunds. Comerford and Edmunds showed that the problem of determining whether or not the class of quadratic exponential equations have solution is decidable, in finitely generated free groups. In this paper we show that for finite systems of quadratic exponential equations decidability passes, under certain hypotheses, from the factor groups to free products and one-relator products.

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