Proceedings of the American Mathematical Society

Author(s): A. A. Ivanov
Journal: Proc. Amer. Math. Soc. 130 (2002), 875-882.
MSC (1991): Primary 03C45
Posted: August 28, 2001
Retrieve article in: PDF
This article is available free of charge

Abstract: We describe permutation groups $G \le Sym(\omega)$ such that

is the closure of the subgroup of all elements with finite support and

can be realized as

where

is a saturated structure. We also study isometric actions of such groups on real trees.

1.: H.Bass, Some remarks on groups acting on trees, Comm. Alg. 4(1976), 1091 - 1126. MR 54:7634
2.: E.Bouscaren and M.C.Laskowski, S-homogeneity and automorphism groups, J. Symb. Logic 58 (1993), 1302 - 1322. MR 95c:03076
3.: R.M.Bryant and D.M.Evans, The small index property for free groups and relatively free groups, J. London Math. Soc. (2) 55 (1997), 363 - 369. MR 97m:20047
4.: C.C.Chang and H.J.Keisler, Model Theory. Studies in Logic, vol. 73, North-Holland, 1973. MR 53:12927
5.: J. Cossey, O.H.Kegel and G.Kovács, Maximal Frattini extensions, Arch. Math. 35 (1980), 210 - 217. MR 82f:20042
6.: M.Culler and K.Vogtmann, A group theoretic criterion for property FA, Proc. Amer. Math. Soc. 124(1996), 677 - 683. MR 96f:20040
7.: D.M.Evans, H.D.Macherson and A.A.Ivanov, Finite covers, in: Model Theory of Groups and Automorphism Groups, (D.M.Evans, ed.), London Math. Soc. Lecture Notes, vol. 244, Cambridge University Press, Cambridge, 1997, pp. 1 - 72. MR 2001a:03075
8.: L.Fuchs, Infinite Abelian Groups, 1 and 2. Academic Press, New York and London, 1971, 1973. MR 50:2362
9.: W.Hodges, I.M.Hodkinson, D.Lascar, S.Shelah, The small index property for $\omega$ -stable $\omega$ -categorical structures and for the random graph, J. London Math. Soc. (2) 48 (1993), 204 - 218. MR 94d:03063
10.: S.Koppelberg and J.Tits, Une propriété des produits directs infinis groupes finis isomorphes, C. R. Acad. Sci. Paris Sér. A 279 (1974), 583 - 585. MR 51:13058
11.: P.M.Neumann, The lawlessness of groups of finitary permutations, Arch. Math. 26 (1975), 561 - 566. MR 54:406
12.: P.M.Neumann, The structure of finitary permutation groups, Arch. Math. 27 (1976), 3 - 17. MR 53:5754
13.: J.Saffe, Categoricity and ranks, J. Symbol. Logic 49 (1984), 1379 - 1392. MR 86a:03034
14.: J. Saxl, S.Shelah and S.Thomas, Infinite products of finite simple groups, Trans. Amer. Math. Soc. 348 (1996), 4611 -4641. MR 97j:20031
15.: J.-P. Serre, Trees. Springer-Verlag, 1980. MR 82e:20083
16.: S.Shelah, Classification Theory. North-Holland, Amsterdam. 1978. MR 81a:03030
17.: J.Tits, A ``theorem of Lie-Kolchin" for trees, Contributions to Algebra: A Collection of Papers dedicated to Ellis Kolchin (H.Bass, P.J.Cassidy and J.Kovacic, eds.), Academic Press, New York, 1977, pp. 377 - 388. MR 58:28205
18.: J.K.Truss, Generic automorphisms of homogeneous structures, Proc. London Math. Soc. (3) 65(1992), 121 - 141. MR 93f:20008

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 03C45

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS