An Application of Word Combinatorics to Decision Problems in Group Theory
In this work we develop a graph theoretical test on graphs corresponding to subgroups of one-relator groups with small cancellation condition which, if successful, implies that the subgroup under consideration has solvable membership problem with a simple solution. The proof of the solvability of the membership problem relies on word combinatorics in an essential way.
Mathematics Subject Classification (2000)Primary 20E06 Secondary 20F05 20F06
KeywordsOne-relator groups small cancellation conditions membership problem Whithead graphs
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