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  1. #1
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    subgroup

    My niece told me that she needed some help... so, here I am begging for yours!

    It's in spanish, so I'll translate as best as possible:

    Let H be a subgroup of a certain group G and a a fixed element of G. Prove that K - the set of all the elements in the form aha^{-1} with h \in H is a subgroup of G.

    K ={ x \in G : x = aha^{-1}, for some h \in H}
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  2. #2
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    Quote Originally Posted by Kimberly View Post
    My niece told me that she needed some help... so, here I am begging for yours!

    It's in spanish, so I'll translate as best as possible:

    Let H be a subgroup of a certain group G and a a fixed element of G. Prove that K - the set of all the elements in the form aha^{-1} with h \in H is a subgroup of G.

    K ={ x \in G : x = aha^{-1}, for some h \in H}
    \forall x,y \in K, x = ah_1a^{-1} , y^{-1} = ah_{2}^{-1}a^{-1} for some h_1, h_2 \in H. xy^{-1} = (ah_1a^{-1})(ah_{2}^{-1}a^{-1}) = ah_1h_{2}^{-1}a^{-1}
    But since H is a subgroup, h_1h_{2}^{-1} \in H
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