Geodesic
A Finite Index Property of Certain Solvable Groups
Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 485-489

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A group G is said to have the FINITE INDEX property (G is an FI-group) if, whenever H≤G, xp ∈ H for some x in G and p > 0, then |〈H, x〉: H| is finite. Following a brief discussion of some locally nilpotent groups with this property, it is shown that torsion-free solvable groups of finite rank which have the isolator property are FI-groups. It is deduced from this that a finitely generated torsion-free solvable group has an FI-subgroup of finite index if and only if it has finite rank.
DOI : 10.4153/CMB-1984-077-3
Mots-clés : 20E34, 20F16 
Rhemtulla, A. H.; Smith, H. A Finite Index Property of Certain Solvable Groups. Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 485-489. doi: 10.4153/CMB-1984-077-3
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     author = {Rhemtulla, A. H. and Smith, H.},
     title = {A {Finite} {Index} {Property} of {Certain} {Solvable} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {485--489},
     year = {1984},
     volume = {27},
     number = {4},
     doi = {10.4153/CMB-1984-077-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-077-3/}
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