Residual finiteness of outer automorphism groups of certain pinched 1-relator groups

[摘要] E. K. Grossman (1974, J. London Math, Soc. 2, 160-164) showed that outer automorphism groups of fundamental groups of closed orientable surfaces are residually finite. Here we generalize her result by showing that outer automorphism groups of generalized free products of two free groups amalgamating a maximal cyclic subgroup are residually finite. From this it follows that mapping class groups of closed orientable and nonorientable surfaces are residually finite. The latter answers a question raised by A. M. Gaglione. (C) 2001 Elsevier Science.

[发布日期] 2001-12-15

[关键词] outer automorphism;residually finite;conjugacy separability;generalized free products;mapping class groups