Geodesic
On the existence of complements in a~group to~some abelian normal subgroups
Algebra and discrete mathematics, Tome 10 (2010) no. 1, pp. 18-41

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

A complement to a proper normal subgroup $H$ of a group $G$ is a subgroup $K$ such that $G=HK$ and $H\cap K=\langle 1\rangle$. Equivalently it is said that $G$ splits over $H$. In this paper we develop a theory that we call hierarchy of centralizers to obtain sufficient conditions for a group to split over a certain abelian subgroup. We apply these results to obtain an entire group-theoretical wide extension of an important result due to D. J. S. Robinson formerly shown by cohomological methods.
Keywords: splitting theorem, hierarchy of centralizers, hyperfinite group, socular series, section rank, $0$-rank.
Mots-clés : Complement, socle of a group 
@article{ADM_2010_10_1_a3,
     author = {Martyn R. Dixon and Leonid A. Kurdachenko and Javier Otal},
     title = {On the existence of complements in a~group to~some abelian normal subgroups},
     journal = {Algebra and discrete mathematics},
     pages = {18--41},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2010_10_1_a3/}
}
TY  - JOUR
AU  - Martyn R. Dixon
AU  - Leonid A. Kurdachenko
AU  - Javier Otal
TI  - On the existence of complements in a~group to~some abelian normal subgroups
JO  - Algebra and discrete mathematics
PY  - 2010
SP  - 18
EP  - 41
VL  - 10
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2010_10_1_a3/
LA  - en
ID  - ADM_2010_10_1_a3
ER  - 
%0 Journal Article
%A Martyn R. Dixon
%A Leonid A. Kurdachenko
%A Javier Otal
%T On the existence of complements in a~group to~some abelian normal subgroups
%J Algebra and discrete mathematics
%D 2010
%P 18-41
%V 10
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2010_10_1_a3/
%G en
%F ADM_2010_10_1_a3
Martyn R. Dixon; Leonid A. Kurdachenko; Javier Otal. On the existence of complements in a~group to~some abelian normal subgroups. Algebra and discrete mathematics, Tome 10 (2010) no. 1, pp. 18-41. http://geodesic.mathdoc.fr/item/ADM_2010_10_1_a3/