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초록· 키워드
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We show that, for any non-zero integers $\la$, $\mu$, $\nu$, $\xi$, class-preserving automorphisms of the group $$G(\la, \mu, \nu, \xi) =\cy{a,b,t: b^{-1} a^{\la} b=a^{\mu}, t^{-1} a^\nu t = b^\xi }$$ are all inner. Hence, by using Grossman's result, the outer automorphism group of $G(\la, \pm\la, \nu, \xi)$ is residually finite.
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참고문헌 (30)
참고문헌 신청
R. B. J. T. Allenby / 2005 / Residual finiteness of outer automorphism groups of finitely generated non-triangle Fuchsian groups / Internat. J. Algebra Comput 15(1):59~72
R. B. J. T. Allenby / 2009 / Outer automorphism groups of Seifert 3-manifold groups over non-orientable surfaces / J. Algebra 322(4):957~968
G. Baumslag / 1969 / A non-cyclic one-relator group all of whose finite quotients are cyclic / J. Austral. Math. Soc 10:497~498
G. Baumslag / 1962 / Some two-generator one-relator non-Hopfian groups / Bull. Amer. Math. Soc 38:199~201
A. V. Borshchev / 2006 / On the isomorphism of some groups with one defining relation / Math. Notes 79(1-2):31~40
R. B. J. T. Allenby / 2009 / Outer automorphism groups of Seifert 3-manifold groups over non-orientable surfaces / J. Algebra 322(4):957~968
G. Baumslag / 1969 / A non-cyclic one-relator group all of whose finite quotients are cyclic / J. Austral. Math. Soc 10:497~498
G. Baumslag / 1962 / Some two-generator one-relator non-Hopfian groups / Bull. Amer. Math. Soc 38:199~201
A. V. Borshchev / 2006 / On the isomorphism of some groups with one defining relation / Math. Notes 79(1-2):31~40
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