In this paper, we give a generalization of Baer Theorem on the injective property of divisible abelian groups. As consequences of the obtained result we find a sufficient condition for a group to express as semi-direct product of a divisible subgroup and some subgroup . We also apply the main Theorem to the -groups with center of index , for some prime . For these groups we compute the number of conjugacy classes and the number of abelian maximal subgroups and the number of nonabelian maximal subgroups.
Mots-clés : Maximal subgroup, divisible groups, p-groups, center, conjugacy classes
@article{AMBP_2009__16_2_267_0, author = {Noui, Lemnouar}, title = {Properties of subgroups not containing their centralizers}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {267--275}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {16}, number = {2}, year = {2009}, doi = {10.5802/ambp.266}, zbl = {1196.20034}, mrnumber = {2568865}, language = {en}, url = {http://www.numdam.org/articles/10.5802/ambp.266/} }
TY - JOUR AU - Noui, Lemnouar TI - Properties of subgroups not containing their centralizers JO - Annales mathématiques Blaise Pascal PY - 2009 SP - 267 EP - 275 VL - 16 IS - 2 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.266/ DO - 10.5802/ambp.266 LA - en ID - AMBP_2009__16_2_267_0 ER -
%0 Journal Article %A Noui, Lemnouar %T Properties of subgroups not containing their centralizers %J Annales mathématiques Blaise Pascal %D 2009 %P 267-275 %V 16 %N 2 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.266/ %R 10.5802/ambp.266 %G en %F AMBP_2009__16_2_267_0
Noui, Lemnouar. Properties of subgroups not containing their centralizers. Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 2, pp. 267-275. doi : 10.5802/ambp.266. http://www.numdam.org/articles/10.5802/ambp.266/
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