On Torsion-Free Groups of Finite Rank
Copyright policy )On Torsion-Free Groups of Finite Rank
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 setWe 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.
- University of Alberta Canada
Solvable groups, supersolvable groups, Chains and lattices of subgroups, subnormal subgroups, finitely generated torsion-free solvable group, subgroup of finite index, Subgroup theorems; subgroup growth, finite rank, isolator property
Solvable groups, supersolvable groups, Chains and lattices of subgroups, subnormal subgroups, finitely generated torsion-free solvable group, subgroup of finite index, Subgroup theorems; subgroup growth, finite rank, isolator property
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