Locally nilpotent groups with all subgroups normal-by-(finite rank)

1998 ◽  
Vol 1 (3) ◽  
Author(s):  
H. Smith ◽  
M. Maj ◽  
P. Longobardi
Keyword(s):  
Finite Rank ◽  
Nilpotent Groups ◽  
Locally Nilpotent Groups ◽  
Locally Nilpotent

A Finite Index Property of Certain Solvable Groups

1984 ◽  
Vol 27 (4) ◽  
pp. 485-489
Author(s):  
A. H. Rhemtulla ◽  
H. Smith
Keyword(s):  
Solvable Group ◽  
Finite Index ◽  
Finite Rank ◽  
Solvable Groups ◽  
Nilpotent Groups ◽  
Finitely Generated ◽  
Free Solvable Group ◽  
Locally Nilpotent Groups ◽  
Locally Nilpotent ◽  
Torsion Free

AbstractA 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.

scholarly journals A finiteness condition on centralizers in locally nilpotent groups

2015 ◽  
Vol 182 (2) ◽  
pp. 289-298 ◽  
Author(s):  
Gustavo A. Fernández-Alcober ◽  
Leire Legarreta ◽  
Antonio Tortora ◽  
Maria Tota
Keyword(s):  
Nilpotent Groups ◽  
Finiteness Condition ◽  
Locally Nilpotent Groups ◽  
Locally Nilpotent
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