Transfer (group theory)

In the mathematical field of group theory, the transfer defines, given a group G and a subgroup H of finite 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 Issai Schur (1902) and rediscovered by Emil Artin (1929).

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