Editing Transfer (group theory) (section)

In the mathematical field of [[group theory]], the '''transfer''' defines, given a [[Group (mathematics)|group]] ''G'' and a [[subgroup]] ''H'' of finite [[Index of a subgroup|index]], a [[group homomorphism]] from ''G'' to the [[abelianization]] of ''H''. It can be used in conjunction with the [[Sylow theorems]] to obtain certain numerical results on the existence of finite simple groups.

The transfer was defined by {{harvs|txt|authorlink=Issai Schur|first=Issai|last= Schur|year=1902}} and rediscovered by {{harvs|txt|first=Emil|last= Artin|authorlink=Emil Artin|year=1929}}.<ref name=S122/>