# zbMATH — the first resource for mathematics

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
Full Text: