Conjugacy separability of certain generalized free products of nilpotent groups
2
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
It is known that generalized free products of finitely gen-erated nilpotent groups are conjugacy separable when the amalgamatedsubgroups are cyclic or central in both factor groups. However, those gen-eralized free products may not be conjugacy separable when the amalga-mated subgroup is a direct product of two infinite cycles. In this paper weshow that generalized free products of finitely generated nilpotent groupsare conjugacy separable when the amalgamated subgroup is <h> × D,where D is in the center of both factors.
Abstract
It is known that generalized free products of finitely gen-erated nilpotent groups are conjugacy separable when the amalgamatedsubgroups are cyclic or central in both factor groups. However, those gen-eralized free products may not be conjugacy separable when the amalga-mated subgroup is a direct product of two infinite cycles. In this paper weshow that generalized free products of finitely generated nilpotent groupsare conjugacy separable when the amalgamated subgroup is <h> × D,where D is in the center of both factors.
참고문헌 (21)
- G. Baumslag, "A non-Hopfian group", Bull. Amer. Math. Soc, 68, pp.196~198 (1962)
- N. Blackburn, "Conjugacy in nilpotent groups", Proc. Amer. Math. Soc, 16, pp.143~148 (1965)
- J. L. Dyer, "Separating conjugates in free-by-finite groups", J. London Math. Soc. (2), 20(2), pp.215~221 (1979)
- J. L. Dyer, "Separating conjugates in amalgamated free products and HNN extensions", J. Austral. Math. Soc. Ser. A, 29(1), pp.35~51 (1980)
- B. Fine, "Conjugacy separability of Fuchsian groups and related ques- tions, Combinatorial group theory", Contemp. Math., 109, pp.11~18 (1990), Amer. Math. Soc.
- E. Formanek, "Conjugate separability in polycyclic groups", J. Algebra, 42(1), pp.1~10 (1976)
- G. Kim, "Conjugacy separability of generalized free products of finite extensions of residually nilpotent groups", Group Theory (Proc. of the ‘96 Beijing Int’l Symposium), pp.10~24 (1998), Springer-Verlag
- G. Kim, "Separability properties of certain tree products of groups", J. Algebra, 251(1), pp.323~349 (2002)
- John C. Lennox, "On products of subgroups in polycyclic groups", Arch. Math, 33(4), pp.305~309 (1979)
- W. Magnus, "Combinatorial Group Theory, Pure and Applied Math. Vol. XIII" (1966), Wiley-Interscience
- A. I. Mal’cev, "Homomorphisms of finite groups", Ivanov Gos. Ped. Inst. U˘cen. Zap. Uchen. Zap. Karel. Ped. Inst. Ser. Fiz.-Mat. Nauk, 18, pp.49~60 (1958)
- A. W. Mostowski, "On the decidability of some problems in special classes of groups", Fund. Math, 59, pp.123~135 (1966)
- G. A. Niblo, "Separability properties of free groups and surface groups", J. Pure and Appl. Algebra, 78(1), pp.77~84 (1992)
- V. N. Remeslennikov, "Conjugacy in polycyclic groups", Algebra Log, 8, pp.712~725 (1969)
- V. N. Remeslennikov, "Groups that are residually finite with respect to conjugacy", Siberian Math. J, 12, pp.783~792 (1971)
- L. Ribes, "Conjugacy separability and free products of groups with cyclic amalgamation", J. London Math. Soc, 57(3), pp.609~628 (1998)
- L. Ribes, "On the profinite topology on a free group", Bull. London Math. Soc, 25(1), pp.37~43 (1993)
- P. Scott, "Subgroups of surface groups are almost geometric", J. London Math. Soc, 17(3), pp.555~565 (1978)
- P. F. Stebe, "A residual property of certain groups", Proc. Amer. Math. Soc, 26, pp.37~42 (1970)
- C. Y. Tang, "Conjugacy separability of generalized free products of surface groups", J. Pure Appl. Algebra, 120(2), pp.187~194 (1997)
- J. S. Wilson, "Conjugacy separability of certain Bianchi groups and HNN extensions", Math. Proc. Cambridge Philos. Soc, 123(2), pp.227~242 (1998)