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In the mathematical field of group theory, the transfer defines, given a group ''G'' and a subgroup of finite index ''H'', 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 and rediscovered by .〔 ==Construction== The construction of the map proceeds as follows:〔Following Scott 3.5〕 Let () = ''n'' and select coset representatives, say : for ''H'' in ''G'', so ''G'' can be written as a disjoint union : Given ''y'' in ''G'', each ''yxi'' is in some coset ''xjH'' and so : for some index ''j'' and some element ''h''''i'' of ''H''. The value of the transfer for ''y'' is defined to be the image of the product : in ''H''/''H''′, where ''H''′ is the commutator subgroup of ''H''. The order of the factors is irrelevant since ''H''/''H''′ is abelian. It is straightforward to show that, though the individual ''hi'' depends on the choice of coset representatives, the value of the transfer does not. It's also straightforward to show that the mapping defined this way is a homomorphism. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Transfer (group theory)」の詳細全文を読む スポンサード リンク
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