Geodesic
Some finiteness conditions concerning intersections of conjugates of subgroups
Glasgow mathematical journal, Tome 37 (1995) no. 3, pp. 327-335

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

In [3], a group G was said to be a CF-group if, for every subgroup H of G, H/CoreGH is finite. It was shown there that a locally finite CF-group G is abelian-by-finite and that there is a bound for the indices |H: CoreGH| as H runs through all subgroups of G. (Groups for which such a bound exists were referred to in [3] as BCF-groups.) The CF-property was further investigated in [10], one of the main results there being that nilpotent CF-groups are (again) abelian-by-finite and BCF. In the present paper, we shall discuss the CF-property in conjunction with some related properties, which are defined as follows. 
Lennox, John C.; Longobardi, Patrizia; Maj, Mercede; Smith, Howard; Wiegold, James. Some finiteness conditions concerning intersections of conjugates of subgroups. Glasgow mathematical journal, Tome 37 (1995) no. 3, pp. 327-335. doi: 10.1017/S0017089500031608
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