Geodesic
Centraliser dimension and universal classes of groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 3 (2006), pp. 197-215

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

In this paper we establish results that will be required for the study of the algebraic geometry of partially commutative groups. We define classes of groups axiomatized by sentences determined by a graph. Among the classes which arise this way we find $\mathrm{CSA}$ and $\mathrm{CT}$ groups. We study the centralisers of a group, with particular attention to the height of the lattice of centralisers, which we call the centraliser dimension of the group. The behaviour of centraliser dimension under several common group operations is described. Groups with centraliser dimension $2$ are studied in detail. It is shown that $\mathrm{CT}$-groups are precisely those with centraliser dimension $2$ and trivial centre. 
@article{SEMR_2006_3_a12,
     author = {Andrew J. Duncan and Ilya V. Kazatchkov and Vladimir N. Remeslennikov},
     title = {Centraliser dimension and universal classes of groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {197--215},
     publisher = {mathdoc},
     volume = {3},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2006_3_a12/}
}
TY  - JOUR
AU  - Andrew J. Duncan
AU  - Ilya V. Kazatchkov
AU  - Vladimir N. Remeslennikov
TI  - Centraliser dimension and universal classes of groups
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2006
SP  - 197
EP  - 215
VL  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2006_3_a12/
LA  - en
ID  - SEMR_2006_3_a12
ER  - 
%0 Journal Article
%A Andrew J. Duncan
%A Ilya V. Kazatchkov
%A Vladimir N. Remeslennikov
%T Centraliser dimension and universal classes of groups
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2006
%P 197-215
%V 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2006_3_a12/
%G en
%F SEMR_2006_3_a12
Andrew J. Duncan; Ilya V. Kazatchkov; Vladimir N. Remeslennikov. Centraliser dimension and universal classes of groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 3 (2006), pp. 197-215. http://geodesic.mathdoc.fr/item/SEMR_2006_3_a12/