We prove that certain 1-relator groups have Property E. Using this fact, we characterize all conjugacy separable 1-relator groups of the form a,b;(a-αbβaαbγ)t , t 1, having residually finite outer automorphism gro...We prove that certain 1-relator groups have Property E. Using this fact, we characterize all conjugacy separable 1-relator groups of the form a,b;(a-αbβaαbγ)t , t 1, having residually finite outer automorphism groups.展开更多
Grossman first showed that outer automorphism groups of 1-relator groups given by orientable surface groups are residually finite,whence mapping class groups of orientable surfaces are residually finite.Allenby,Kim an...Grossman first showed that outer automorphism groups of 1-relator groups given by orientable surface groups are residually finite,whence mapping class groups of orientable surfaces are residually finite.Allenby,Kim and Tang showed that outer automorphism groups of cyclically pinched 1-relator groups are residually finite,whence mapping class groups of orientable and non-orientable surfaces are residually finite.In this paper we show that outer automorphism groups of certain conjugacy separable 1-relator groups are residually finite.展开更多
基金supported by Korean Research Foundation funded by the Korean Government (Grant No. KRF-2007-313-C00015)The second author was supported by Natural Science and Engineering Research Council of Canada (Grant No. A-4064)
文摘We prove that certain 1-relator groups have Property E. Using this fact, we characterize all conjugacy separable 1-relator groups of the form a,b;(a-αbβaαbγ)t , t 1, having residually finite outer automorphism groups.
基金supported by the Korean Research Foundation from the Korean Government (Grant No.KRF-2008-313-C00017)the partial support by the Natural Science and Engineering Research Council of Canada (Grant No.A-4064)
文摘Grossman first showed that outer automorphism groups of 1-relator groups given by orientable surface groups are residually finite,whence mapping class groups of orientable surfaces are residually finite.Allenby,Kim and Tang showed that outer automorphism groups of cyclically pinched 1-relator groups are residually finite,whence mapping class groups of orientable and non-orientable surfaces are residually finite.In this paper we show that outer automorphism groups of certain conjugacy separable 1-relator groups are residually finite.
