Geodesic
Groups of Automorphisms and Chains of Closed Subgroups
Matematičeskie trudy, Tome 4 (2001) no. 2, pp. 128-137 
K. Zh. Kudaibergenov. Groups of Automorphisms and Chains of Closed Subgroups. Matematičeskie trudy, Tome 4 (2001) no. 2, pp. 128-137. http://geodesic.mathdoc.fr/item/MT_2001_4_2_a6/
@article{MT_2001_4_2_a6,
     author = {K. Zh. Kudaibergenov},
     title = {Groups of {Automorphisms} and {Chains} of {Closed} {Subgroups}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {128--137},
     year = {2001},
     volume = {4},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2001_4_2_a6/}
}
TY  - JOUR
AU  - K. Zh. Kudaibergenov
TI  - Groups of Automorphisms and Chains of Closed Subgroups
JO  - Matematičeskie trudy
PY  - 2001
SP  - 128
EP  - 137
VL  - 4
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MT_2001_4_2_a6/
LA  - ru
ID  - MT_2001_4_2_a6
ER  - 
%0 Journal Article
%A K. Zh. Kudaibergenov
%T Groups of Automorphisms and Chains of Closed Subgroups
%J Matematičeskie trudy
%D 2001
%P 128-137
%V 4
%N 2
%U http://geodesic.mathdoc.fr/item/MT_2001_4_2_a6/
%G ru
%F MT_2001_4_2_a6

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

The problem is studied of the possibility of representing the automorphism group of a model as the union of an increasing chain of given length consisting of proper subgroups of a certain type (for instance, closed).

[1] Bhattacharjee M., Macpherson D., Möller R. G., Neumann P. M., Notes on Infinite Permutation Groups, Lecture Notes in Math., 1698, Springer-Verlag, Berlin, etc., 1998 | MR | Zbl

[2] Hodges W., Model Theory, Cambridge Univ. Press, Cambridge, 1993 | MR | Zbl

[3] Hodges W., Hodkinson I., Lascar D., Shelah S., “The small index property for $\omega$-stable $\omega$-categorical structures and for the random graph”, J. London Math. Soc. (2), 48 (1993), 204–218 | DOI | MR | Zbl

[4] Macpherson H. D., Neumann P. M., “Subgroups of infinite symmetric groups”, J. London Math. Soc. (2), 42 (1990), 64–84 | DOI | MR | Zbl