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The residual finiteness of negatively curved polygons of finite groups. (English) Zbl 1040.20024
A subgroup \(M\) of a group \(G\) is called malnormal if for each \(g\in G\setminus M\), \(M\cap M^g\) is trivial. The subgroup \(M\) is almost malnormal if for each \(g\in G\setminus M\), \(M\cap M^g\) is finite. This paper is concerned with the question of M. Gromov [Publ., Math. Sci. Res. Inst. 8, 75–263 (1987; Zbl 0634.20015)] as to whether every word hyperbolic group is residually finite. The author proves that if \(G=A*_MB\) is an amalgamated free product, where \(A,B\) are virtually free and \(M\) is a finitely generated almost malnormal subgroup of \(A\) and \(B\) then \(G\) is residually finite. This is a special case of the main result which establishes residual finiteness when \(G\) splits as a graph of virtually free groups satisfying a similar condition.

MSC:
20E26 Residual properties and generalizations; residually finite groups
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20F67 Hyperbolic groups and nonpositively curved groups
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