Titlebook: Combinatorial and Geometric Group Theory; Dortmund and Ottawa- Oleg Bogopolski,Inna Bumagin,Enric Ventura Conference proceedings 2010 Birkh

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An Application of Word Combinatorics to Decision Problems in Group Theory,f 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.

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,Limits of Thompson’s Group ,,e .., (.., x.) ∈ . ∈ N, be a family of groups isomorphic to . and marked by .+2 elements. If the sequence (..). is convergent in the space of marked groups and G is the corresponding limit we say that . is an .-limit group. The paper is devoted to a description of .-limit groups.

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