Properties of subgroups not containing their centralizers
Noui, Lemnouar
Annales mathématiques Blaise Pascal, Tome 16 (2009), p. 267-275 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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 G to express as semi-direct product of a divisible subgroup D and some subgroup H. We also apply the main Theorem to the p-groups with center of index p 2 , for some prime p. For these groups we compute N c (G) the number of conjugacy classes and N a the number of abelian maximal subgroups and N na the number of nonabelian maximal subgroups.

Publié le : 2009-01-01
DOI : https://doi.org/10.5802/ambp.266
Classification:  14L05,  20D25,  20K27,  20E28 
@article{AMBP_2009__16_2_267_0,
     author = {Noui, Lemnouar},
     title = {Properties of subgroups not containing their centralizers},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {16},
     year = {2009},
     pages = {267-275},
     doi = {10.5802/ambp.266},
     zbl = {1196.20034},
     mrnumber = {2568865},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AMBP_2009__16_2_267_0}
}

Noui, Lemnouar. Properties of subgroups not containing their centralizers. Annales mathématiques Blaise Pascal, Tome 16 (2009) pp. 267-275. doi : 10.5802/ambp.266. http://gdmltest.u-ga.fr/item/AMBP_2009__16_2_267_0/

[1] Reid, Michael The number of conjugacy classes, Amer. Math. Monthly, Tome 105 (1998) no. 4, pp. 359-361 | Article | MR 1614889 | Zbl 0924.20015

[2] Robinson, Derek J. S. Finiteness conditions and generalized soluble groups. Part 1, Springer-Verlag, New York (1972) (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 62) | MR 332989 | Zbl 0243.20032

[3] Robinson, Derek J. S. A course in the theory of groups, Springer-Verlag, New York, Graduate Texts in Mathematics, Tome 80 (1996) | MR 1357169 | Zbl 0836.20001

[4] Sherman, Gary A lower bound for the number of conjugacy classes in a finite nilpotent group, Pacific J. Math., Tome 80 (1979) no. 1, p. 253-254 | MR 534714 | Zbl 0377.20017

[5] Watson, N. Subgroups of finite abelian groups (1995) (Summer research paper, Haverford College)