Geodesic
A Property of Groups with No Central Factors
Canadian mathematical bulletin, Tome 12 (1969) no. 4, pp. 467-470

Voir la notice de l'article provenant de la source Cambridge University Press

Let C1 denote the class of all groups with no non-trivial central factors. We prove the following theoremThere exist non-trivial locally solvable C1 groups; but there is no non-trivial locally k-step polynilpotent C1 group for any integer k.It is well known that a minimal normal subgroup of a locally solvable group is abelian. Thus no non-trivial locally solvable group can be pluperfect - the class of all perfect groups in which every subnormal subgroup is also perfect. 
Rhemtulla, A. H. A Property of Groups with No Central Factors. Canadian mathematical bulletin, Tome 12 (1969) no. 4, pp. 467-470. doi: 10.4153/CMB-1969-058-6
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