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Full-Text Articles in Physical Sciences and Mathematics
The Two Variable Substitution Problem For Free Products Of Groups, Leo P. Comerford, Charles C. Edmunds
The Two Variable Substitution Problem For Free Products Of Groups, Leo P. Comerford, Charles C. Edmunds
Leo Comerford
We consider equations of the form W(x,y) = U with U an element of a free product G of groups. We show that with suitable algorithmic conditions on the free factors of G, one can effectively determine whether or not the equations have solutions in G. We also show that under certain hypotheses on the free factors of G and the equation itself, the equation W(x,y) = U has only finitely many solutions, up to the action of the stabilizer of W(x,y) in Aut().
Commutators As Powers In Free Products Of Groups, Leo Comerford, Charles C. Edmunds, Gerhard Rosenberger
Commutators As Powers In Free Products Of Groups, Leo Comerford, Charles C. Edmunds, Gerhard Rosenberger
Leo Comerford
The ways in which a nontrivial commutator can be a proper power in a free product of groups are identified