Cosets and Lagrange’s Theorem
نویسنده
چکیده
In other words, a coset is what we get when we take a subgroup and shift it (either on the left or on the right). The best way to think about cosets is that they are shifted subgroups, or translated subgroups. Note g lies in both gH and Hg, since g = ge = eg. Typically gH 6= Hg. When G is abelian, though, left and right cosets of a subgroup by a common element are the same thing. When an abelian group operation is written additively, an H-coset should be written as g +H, which is the same as H + g.
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