Left-transitively complemented normal subgroup

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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 a left-transitively complemented normal subgroup if whenever the whole group is a complemented normal subgroup of a bigger group, the subgroup is also a complemented normal subgroup of that group.

Definition with symbols

A subgroup H of a group G is termed a left-transitively complemented normal subgroup if, for any group K containing G such that G is a complemented normal subgroup of K, then H is also a complemented normal subgroup of K.

Formalisms

In terms of the left transiter

This property is obtained by applying the left transiter to the property: complemented normal subgroup
View other properties obtained by applying the left transiter

Relation with other properties

Stronger properties

Weaker properties

Related properties