On Certain 3-Generator Artin Groups
Copyright policy )On Certain 3-Generator Artin Groups
The author considers three infinite 3-generator Artin groups \[ S= \] \[ T= \] \[ U=. \] Their Coxeter diagrams are the smallest for which the groups are infinite. The main result is that S, T, and U are semidirect products of a free group of countable, infinite rank with an appropriate 2-generator Artin group. S is also an HNN extension of a free group of rank 2 by an automorphism of a subgroup index 2. T and U are both free products with amalgamation of a free group of rank 4 and another of rank 3 amalgamated along a free subgroup of rank 7. As a consequence, the word problems of S, T, and U are solvable (T was known to have a solvable word problem).
Generators, relations, and presentations of groups, Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Coxeter diagrams, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), infinite 3-generator Artin groups, semidirect products, HNN extension, Geometric group theory, free products with amalgamation, solvable word problem
Generators, relations, and presentations of groups, Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Coxeter diagrams, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), infinite 3-generator Artin groups, semidirect products, HNN extension, Geometric group theory, free products with amalgamation, solvable word problem
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