Geodesic
ON SOLUBILITY OF GROUPS WITH BOUNDED CENTRALIZER CHAINS
Glasgow mathematical journal, Tome 51 (2009) no. 1, pp. 49-54

Voir la notice de l'article provenant de la source Cambridge University Press

The c-dimension of a group is the maximum length of a chain of nested centralizers. It is proved that a periodic locally soluble group of finite c-dimension k is soluble of derived length bounded in terms of k, and the rank of its quotient by the Hirsch–Plotkin radical is bounded in terms of k. Corollary: a pseudo-(finite soluble) group of finite c-dimension k is soluble of derived length bounded in terms of k.
DOI : 10.1017/S0017089508004527
Mots-clés : Primary: 20D10, Secondary: 03C20, 20D45, 20F16, 20F22 
KHUKHRO, E. I. ON SOLUBILITY OF GROUPS WITH BOUNDED CENTRALIZER CHAINS. Glasgow mathematical journal, Tome 51 (2009) no. 1, pp. 49-54. doi: 10.1017/S0017089508004527
@article{10_1017_S0017089508004527,
     author = {KHUKHRO, E. I.},
     title = {ON {SOLUBILITY} {OF} {GROUPS} {WITH} {BOUNDED} {CENTRALIZER} {CHAINS}},
     journal = {Glasgow mathematical journal},
     pages = {49--54},
     year = {2009},
     volume = {51},
     number = {1},
     doi = {10.1017/S0017089508004527},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004527/}
}
TY  - JOUR
AU  - KHUKHRO, E. I.
TI  - ON SOLUBILITY OF GROUPS WITH BOUNDED CENTRALIZER CHAINS
JO  - Glasgow mathematical journal
PY  - 2009
SP  - 49
EP  - 54
VL  - 51
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004527/
DO  - 10.1017/S0017089508004527
ID  - 10_1017_S0017089508004527
ER  - 
%0 Journal Article
%A KHUKHRO, E. I.
%T ON SOLUBILITY OF GROUPS WITH BOUNDED CENTRALIZER CHAINS
%J Glasgow mathematical journal
%D 2009
%P 49-54
%V 51
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004527/
%R 10.1017/S0017089508004527
%F 10_1017_S0017089508004527

[1] 1.Berger, T. R. and Gross, F., 2-length and the derived length of a Sylow 2-subgroup, Proc. Lond. Math. Soc. 34 (3) (1977), 520–534. Google Scholar | DOI

[2] 2.Bludov, V. V., On locally nilpotent groups with the minimality condition for centralizers, Algebra Logika 37 (1998), 270–278; English transl. in Algebra and Logic (1998), 151–156. Google Scholar | DOI

[3] 3.Bryant, R. M., Groups with minimal condition on centralizers, J. Algebra 60 (1979), 371–383. Google Scholar | DOI

[4] 4.Bryant, R. M. and Hartley, B., Periodic locally soluble groups with the minimal condition on centralizers, J. Algebra 61 (1979), 328–334. Google Scholar | DOI

[5] 5.Bryukhanova, E. G., Connection between the 2-length and the derived length of a Sylow 2-subgroup of a finite solvable group, Mat. Zametki 29 (1981), 161–170; English transl. in Math. Notes (1981), 85–90. Google Scholar

[6] 6.Derakhshan, J. and Wagner, F. O., Nilpotency in groups with chain conditions, Quart. J. Math. Oxford 48 (1997), 453–468. Google Scholar | DOI

[7] 7.Duncan, A. J., Kazachkov, I. V. and Remeslennikov, V. N., Centraliser dimension and universal classes of groups, Siberian Electronic Math. Rep. 3 (2006), 197–215; http://semr.math.nsc.ru. Google Scholar

[8] 8.Hall, P. and Higman, G., On the p-length of p-soluble groups and reduction theorems for Burnside's problem, Proc. Lond. Math. Soc. 6 (3) (1956), 1–42. Google Scholar | DOI

[9] 9.Kegel, O., Four lectures on Sylow theory in locally finite groups, in Group Theory Proc. Int. Conf. Singapore, 1987, Walter de Gruyter, Amsterdam, 1989, pp. 3–27. Google Scholar | DOI

[10] 10.Kovács, L. G., On finite soluble groups, Math. Z. 103 (1968), 37–39. Google Scholar | DOI

[11] 11.Macpherson, D. and Tent, K., Stable pseudofinite groups, J. Algebra 312 (2007), 550–561. Google Scholar | DOI

[12] 12.Myasnikov, A. and Shumyatsky, P., Discriminating groups and c-dimension, J. Group Theory 7 (2004), 135–142. Google Scholar

[13] 13.Thompson, J., Automorphisms of solvable groups, J. Algebra 1 (1964), 259–267. Google Scholar | DOI

[14] 14.Wagner, F. O., Stable groups, mostly of finite exponent, Notre Dame J. Formal Logic 34 (1993) 183–192. Google Scholar | DOI

[15] 15.Wagner, F. O., Nilpotency in groups with the minimal condition on centralizers, J. Algebra 217 (1999), 448–460. Google Scholar | DOI

[16] 16.Wilson, J. S., On pseudofinite simple groups, J. Lond. Math. Soc. 51 (2) (1995), 471–490. Google Scholar | DOI

Cité par Sources :