Hereditarily permutable subgroup

From Groupprops
Jump to: navigation, search
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

Symbol-free definition

A subgroup of a group is termed hereditarily permutable if every subgroup of that subgroup is a permutable subgroup in the whole group.

Definition with symbols

A subgroup H of a group G is termed hereditarily permutable in G if whenever K \le H, K is a permutable subgroup of G.

Formalisms

In terms of the hereditarily operator

This property is obtained by applying the hereditarily operator to the property: permutable subgroup
View other properties obtained by applying the hereditarily operator

Relation with other properties

Stronger properties

Weaker properties

Facts