DefinitionFacts
 Schreier's lemma shows that any subgroup of finite index in a finitely generated group is itself finitely generated, and gives an upper bound on the minimum size of generating set in terms of the corresponding value for the whole group.
Relation with other properties
Stronger properties
Property 
Meaning 
Proof of implication 
Proof of strictness (reverse implication failure) 
Intermediate notions


Subgroup of finite group 




Weaker properties
Property 
Meaning 
Proof of implication 
Proof of strictness (reverse implication failure) 
Intermediate notions


Subgroup of finite index 



