Editing Transfer (group theory) (section)

==Construction==
The construction of the map proceeds as follows:<ref>Following Scott 3.5</ref> Let [''G'':''H''] = ''n'' and select [[coset]] [[Artin transfer (group theory)#Transversals of a subgroup|representatives]], say 
:<math>x_1, \dots, x_n,\,</math>
for ''H'' in ''G'', so ''G'' can be written as a disjoint union
:<math>G = \bigcup\ x_i H.</math>
Given ''y'' in ''G'', each ''yx<sub>i</sub>'' is in some coset ''x<sub>j</sub>H'' and so 
:<math>yx_i = x_jh_i</math>
for some index ''j'' and some element ''h''<sub>''i''</sub> of ''H''. 
The value of the transfer for ''y'' is defined to be the image of the product 
:<math>\textstyle \prod_{i=1}^n h_i </math>
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 [[Artin transfer (group theory)#Independence of the transversal|straightforward]] to show that, though the individual ''h<sub>i</sub>'' depends on the choice of coset representatives, the value of the transfer does not. It is also [[Artin transfer (group theory)#Homomorphisms|straightforward]] to show that the mapping defined this way is a homomorphism.