# On minimal non-PC-groups

Francesco Russo^{[1]}; Nadir Trabelsi^{[2]}

- [1] Mathematics Department, University of Naples Federico II via Cinthia, Naples, 80126, Italy
- [2] Laboratory of fundamental and numerical Mathematics, Mathematics Department University Ferhat Abbas, Setif, 19000, Algeria

Annales mathématiques Blaise Pascal (2009)

- Volume: 16, Issue: 2, page 277-286
- ISSN: 1259-1734

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topRusso, Francesco, and Trabelsi, Nadir. "On minimal non-PC-groups." Annales mathématiques Blaise Pascal 16.2 (2009): 277-286. <http://eudml.org/doc/10580>.

@article{Russo2009,

abstract = {A group $G$ is said to be a PC-group, if $G/C_\{G\}(x^\{G\})$ is a polycyclic-by-finite group for all $x\in G$. 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.},

affiliation = {Mathematics Department, University of Naples Federico II via Cinthia, Naples, 80126, Italy; Laboratory of fundamental and numerical Mathematics, Mathematics Department University Ferhat Abbas, Setif, 19000, Algeria},

author = {Russo, Francesco, Trabelsi, Nadir},

journal = {Annales mathématiques Blaise Pascal},

keywords = {Polycyclic-by-finite conjugacy classes; minimal non-PC-groups; locally graded groups; PC-groups; minimal non-PC groups; polycyclic-by-finite groups; subgroups of finite index},

language = {eng},

month = {7},

number = {2},

pages = {277-286},

publisher = {Annales mathématiques Blaise Pascal},

title = {On minimal non-PC-groups},

url = {http://eudml.org/doc/10580},

volume = {16},

year = {2009},

}

TY - JOUR

AU - Russo, Francesco

AU - Trabelsi, Nadir

TI - On minimal non-PC-groups

JO - Annales mathématiques Blaise Pascal

DA - 2009/7//

PB - Annales mathématiques Blaise Pascal

VL - 16

IS - 2

SP - 277

EP - 286

AB - A group $G$ is said to be a PC-group, if $G/C_{G}(x^{G})$ is a polycyclic-by-finite group for all $x\in G$. 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.

LA - eng

KW - Polycyclic-by-finite conjugacy classes; minimal non-PC-groups; locally graded groups; PC-groups; minimal non-PC groups; polycyclic-by-finite groups; subgroups of finite index

UR - http://eudml.org/doc/10580

ER -

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