Free-quotient subgroup

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]

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Definition

A normal subgroup of a group is termed a free-quotient subgroup if it satisfies the following equivalent conditions:

1. The quotient group is a free group.
2. It is a complemented normal subgroup and has a complement that is a free group.

Relation with other properties

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Complemented normal subgroup
Normal subgroup				|FULL LIST, MORE INFO