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Left and Right Cosets in Abelian Groups watch

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    Are the left and right cosets in abelian groups the same??

    Also if the binary operation for a group is addition not multiplication, how do you find the left and right cosets?? Are they the same under addition for both abelian and non-abelian groups??

    Thank you for any help given.
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    (Original post by adie_raz)
    Are the left and right cosets in abelian groups the same??

    Also if the binary operation for a group is addition not multiplication, how do you find the left and right cosets?? Are they the same under addition for both abelian and non-abelian groups??

    Thank you for any help given.
    Yes.

    And the plus sign is just a symbol. You find them in exactly the same way as with a dot symobol (or no symbol). ie, you just "do the operation". More often than not, + is commutative so the group will be abelian. But you could, for example, use + as the operation to compose functions (it'd be weird but it's not forbidden). In which case the group wouldn't be abelian.
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Updated: March 26, 2011
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