Free-quotient subgroup

From Groupprops
Jump to: navigation, search
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]
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]


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