Atlas: Exponential quadratic equations in one-relator products and hyperbolic groups by Andrew Duncan

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G^3 = Geometric Groups on the Gulf coast
March 4-5, 2000
University of South Alabama
Mobile, AL, USA

Organizers
Phil Bowers, Stephen Brick, Jon Corson, Igor Mineyev

Exponential quadratic equations in one-relator products and hyperbolic groups
by
Andrew Duncan
University of Newcastle
Coauthors: Karren Friel (University of Newcastle)

The power problem for a presentation < X|R > of a group G asks whether, given a word w in F(X), there exists a non-zero integer n with wⁿ=1 in G. The power conjugacy problem asks whether, given words u and v F(X), there exist non-zero integers m, n and a word z in F(X) such that z^-1u^mz=vⁿ in G. Continuing to generalize these problems we obtain the class of exponential quadratic equations. Results of Comerford and Edmunds show that this class of problem is decidable for free groups and for free products of free groups with cyclic amalgamation. The talk addresses the decidability of this class of problems in one-relator products of groups and in Hyperbolic groups.

Andrew Duncan

Date received: January 26, 2000