Characteristic subgroup of direct factor

From Groupprops
Jump to: navigation, search
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: characteristic subgroup and direct factor
View other such compositions|View all subgroup properties


Definition

Symbol-free definition

A subgroup of a group is said to be a characteristic subgroup of direct factor if it occurs as a characteristic subgroup of a direct factor of the whole group.

Definition with symbols

A subgroup H of a group G is said to be a characteristic subgroup of direct factor if there are subgroups K,L such that H is characteristic in K, and K \times L = G.

Relation with other properties

Stronger properties

Weaker properties