Local embeddability
Algebra and discrete mathematics, Tome 14 (2012) no. 1, pp. 14-28.

Voir la notice de l'article provenant de la source Math-Net.Ru

For an arbitrary class of algebraic structures we consider a notion of a structure locally embeddable to structures of the class. This generalizes the notion of a group locally embeddable to finite groups studied by Vershik and Gordon. We give various model-theoretic characterizations of such structures. Some of them generalize known group-theoretic results.
Keywords: local embeddability, universal theory
Mots-clés : ultraproduct, limit structure.
@article{ADM_2012_14_1_a2,
     author = {Oleg Belegradek},
     title = {Local embeddability},
     journal = {Algebra and discrete mathematics},
     pages = {14--28},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2012},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/ADM_2012_14_1_a2/}
}
TY  - JOUR
AU  - Oleg Belegradek
TI  - Local embeddability
JO  - Algebra and discrete mathematics
PY  - 2012
SP  - 14
EP  - 28
VL  - 14
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/ADM_2012_14_1_a2/
LA  - en
ID  - ADM_2012_14_1_a2
ER  - 
%0 Journal Article
%A Oleg Belegradek
%T Local embeddability
%J Algebra and discrete mathematics
%D 2012
%P 14-28
%V 14
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/ADM_2012_14_1_a2/
%G en
%F ADM_2012_14_1_a2
Oleg Belegradek. Local embeddability. Algebra and discrete mathematics, Tome 14 (2012) no. 1, pp. 14-28. https://geodesic-test.mathdoc.fr/item/ADM_2012_14_1_a2/

[1] C. Champetier, “L'espace des groupes de type fini”, Topology, 39 (2000), 657–680 | DOI | MR | Zbl

[2] C. Champetier, V. Guirardel, “Limit groups as limits of free groups”, Israel J. Math., 146 (2005), 1–75 | DOI | MR | Zbl

[3] R. Grigorchuk, “Degrees of growth of finitely generated groups and the theory of invariant means”, Izv. Akad. Nauk SSSR Ser. Mat., 48 (1984), 939–985 | MR

[4] W. Hodges, Model theory, Cambridge University Press, Cambridge, 1993 | MR | Zbl

[5] P. T. Johnstone, Stone Spaces, Cambridge University Press, Cambridge, 1982 | MR

[6] A. I. Mal'cev, “On a general method for obtaining local theorems in group theory”, Ivanov. Gos. Ped. Inst. Uc. Zap. Fiz.-Mat. Fak., 1:1 (1941), 3–9 | MR

[7] A. I. Mal'cev, Algebraic systems, Springer-Verlag, New York–Heidelberg, 1973 | MR

[8] A. M. Stëpin, “Approximability of groups and group actions”, Uspekhi Mat. Nauk, 38:6 (1983), 123–124 | MR | Zbl

[9] A. M. Stëpin, “A remark on the approximability of groups”, Vestnik Moskov. Univ. Ser. I. Mat. Mekh., 1984, no. 4, 85–87 | MR | Zbl

[10] V. G. Pestov, Hyperlinear and sofic groups: a brief guide, August 2008, arXiv: 0804.3968v8[math.GR] | MR

[11] V. G. Pestov, A. Kwiatkowska, An introduction to hyperlinear and sofic groups, April 2012, arXiv: 0911.4266v4[math.GR]

[12] A. M. Vershik, E. I. Gordon, “Groups that are locally embeddable in the class of finite groups”, Algebra i Analiz, 9:1 (1997), 71–97 | MR | Zbl