Subgroup of solvable group

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This article describes a property that arises as the conjunction of a subgroup property: subgroup with a group property imposed on the ambient group: solvable group
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

Definition

A subgroup H of a group G is termed a subgroup of solvable group if the whole group G is a solvable group.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
subgroup of abelian group Subgroup of nilpotent group|FULL LIST, MORE INFO
subgroup of nilpotent group Normal subgroup of nilpotent group|FULL LIST, MORE INFO