Finite elliptic subgroup

This article describes a property that arises as the conjunction of a subgroup property: elliptic subgroup with a group property (itself viewed as a subgroup property): finite group
View a complete list of such conjunctions

Definition

A subgroup of a group is termed a finite elliptic subgroup if it is a finite subgroup (i.e., is a finite group in its own right) and is an elliptic subgroup of the whole group.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
finite characteristic subgroup	finite and a characteristic subgroup
finite normal subgroup	finite and a normal subgroup
finite permutable subgroup	finite and a permutable subgroup
subgroup of finite group	the whole group is finite

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
finite subgroup
elliptic subgroup
join-transitively finite subgroup