On minimal non-PC-groups
[Sur les non-PC-groupes minimaux]
Russo, Francesco ; Trabelsi, Nadir
Annales mathématiques Blaise Pascal, Tome 16 (2009), p. 277-286 / Harvested from Numdam
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On dit qu’un groupe G est un PC-groupe, si pour tout x∈G, G/C G (x G ) est une extension d’un groupe polycyclique par un groupe fini. Un non-PC-groupe minimal est un groupe qui n’est pas un PC-groupe mais dont tous les sous-groupes propres sont des PC-groupes. Notre principal résultat est qu’un non-PC-groupe minimal ayant un groupe quotient fini non-trivial est une extension cyclique finie d’un groupe abélien divisible de rang fini.

A group G is said to be a PC-group, if G/C G (x G ) is a polycyclic-by-finite group for all x∈G. A minimal non-PC-group is a group which is not a PC-group but all of whose proper subgroups are PC-groups. Our main result is that a minimal non-PC-group having a non-trivial finite factor group is a finite cyclic extension of a divisible abelian group of finite rank.

Publié le : 2009-01-01
DOI : https://doi.org/10.5802/ambp.267
Classification:  20F24,  20F15,  20E34,  20E45 
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     author = {Russo, Francesco and Trabelsi, Nadir},
     title = {On minimal non-PC-groups},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {16},
     year = {2009},
     pages = {277-286},
     doi = {10.5802/ambp.267},
     zbl = {1187.20042},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AMBP_2009__16_2_277_0}
}

Russo, Francesco; Trabelsi, Nadir. On minimal non-PC-groups. Annales mathématiques Blaise Pascal, Tome 16 (2009) pp. 277-286. doi : 10.5802/ambp.267. http://gdmltest.u-ga.fr/item/AMBP_2009__16_2_277_0/

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