Geodesic
On Torsion-Free Groups of Finite Rank
Canadian journal of mathematics, Tome 36 (1984) no. 6, pp. 1067-1080

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

This paper deals with two conditions which, when stated, appear similar, but when applied to finitely generated solvable groups have very different effect. We first establish the notation before stating these conditions and their implications. If H is a subgroup of a group G, let denote the set We say G has the isolator property if is a subgroup for all H ≦ G. Groups possessing the isolator property were discussed in [2]. If we define the relation ∼ on the set of subgroups of a given group G by the rule H ∼ K if and only if , then ∼ is an equivalence relation and every equivalence class has a maximal element which may not be unique. If , we call H an isolated subgroup of G. 
Meier, David; Rhemtulla, Akbar. On Torsion-Free Groups of Finite Rank. Canadian journal of mathematics, Tome 36 (1984) no. 6, pp. 1067-1080. doi: 10.4153/CJM-1984-061-1
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[1] 1. Hall, P., Some sufficient conditions for a group to be nilpotent, Illinois J. Math. 2 (1958), 787–801. Google Scholar

[2] 2. Rhemtulla, A. H. and Wehrfritz, B. A. F., Isolators in soluble groups of finite rank, Rocky Mountain J. Math. 14 (1984), 415–422. Google Scholar

[3] 3. Rhemtulla, A. H., Weiss, A. and Yousif, M., Solvable groups with π-isolators, Proc. Amer. Math Soc. 90 (1984), 173–178. Google Scholar

[4] 4. Robinson, D. J. S., Finiteness conditions and generalized soluble groups, Parts 1 and 2 (Springer Verlag, 1972). Google Scholar | DOI

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