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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The word problem and related results for graph product groups


Author: K. J. Horadam
Journal: Proc. Amer. Math. Soc. 82 (1981), 157-164
MSC: Primary 20F10; Secondary 03D40, 05C25, 20L10
DOI: https://doi.org/10.1090/S0002-9939-1981-0609643-1
MathSciNet review: 609643
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Abstract: A graph product is the fundamental group of a graph of groups. Amongst the simplest examples are HNN groups and free products with amalgamation.

The torsion and conjugacy theorems are proved for any group presented as a graph product. The graphs over which some graph product has a solvable word problem are characterised. Conditions are then given for the solvability of the word and order problems and also for the extended word problem for cyclic subgroups of any graph product. These results generalise the known ones for HNN groups and free products with amalgamation.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0609643-1
Keywords: Groupoid, graph of groups, fundamental group, word problem, extended word problem, torsion theorem, conjugacy theorem
Article copyright: © Copyright 1981 American Mathematical Society