Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
strongly bounded groups; existentially closed groups
strongly bounded groups; existentially closed groups
Summary:
Let $G$ be a non-trivial algebraically closed group and $X$ be a subset of $G$ generating $G$ in infinitely many steps. We give a construction of a binary tree associated with $(G,X)$. Using this we show that if $G$ is $\omega_1$-existentially closed then it is strongly bounded.
References:
[1] Bergman G.: Generating infinite symmetric groups. Bull. London Math. Soc. 38 (2006), 429-440. MR 2239037 | Zbl 1103.20003
[2] de Cornulier Y.: Strongly bounded groups and infinite powers of finite groups. Comm. Algebra 34 (2006), 2337-2345. MR 2240370 | Zbl 1125.20023
[3] de la Harpe P., Valette A.: La propriété (T) de Kazhdan pour les groupes localement compacts. Astérisque 175, SMF, 1989. Zbl 0759.22001
[4] Hodges W.: Building Models by Games. Cambridge University Press, Cambridge, 1985. MR 0812274 | Zbl 0569.03015
[5] Hodges W., Hodkinson I., Lascar D., Shelah S.: The small index property for $ømega$-stable $ømega$-categorical structures and for the random graph. J. London Math. Soc. (2) 48 (1993), 204-218. MR 1231710 | Zbl 0788.03039
[6] Ivanov A.: Strongly bounded automorphism groups. Colloq. Math. 105 (2006), 57-67. MR 2242499 | Zbl 1098.20003
[7] Kechris A., Rosendal Ch.: Turbulence, amalgamation and generic automorphisms of homogeneous structures. to appear in Proc. London Math. Soc. (arXiv:math.LO/0409567 v3 18 Oct 2004). MR 2308230 | Zbl 1118.03042
[8] Macintyre A.: Model completeness. in: Handbook of Mathematical Logic (edited by Jon Barwise), North-Holland, Amsterdam, 1977, pp.139-180. MR 0457132 | Zbl 0317.02065
[9] Scott W.R.: Algebraically closed groups. Proc. Amer. Math. Soc. 2 (1951), 118-121. MR 0040299 | Zbl 0043.02302
[10] Ziegler M.: Algebraisch abgeschlossene Gruppen. in: World Problems II (edited by S. Adian et al.), North-Holland, 1980, pp.449-576. MR 0579957 | Zbl 0451.20001
Search
Partner of
