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Math Help - Question about subgroups.

  1. #1
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    Question about subgroups.

    If we say that G is a group under *, and k is assume to be a subset, in order to prove that k is a subgroup, we need to find the closure, ID, and inverse.....
    My quetion for closure is, do we let for example the elements g_1,g_2\in G and then show that g_1*g_2\in k,
    Id=e. e\in g then e\in k,?
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    Quote Originally Posted by mancillaj3 View Post
    If we say that G is a group under *, and k is assume to be a subset, in order to prove that k is a subgroup, we need to find the closure, ID, and inverse.....
    My quetion for closure is, do we let for example the elements g_1,g_2\in G and then show that g_1*g_2\in k,
    Id=e. e\in g then e\in k,?
    a subset K of a group is a subgroup if and only if \forall a,b \in K: \ ab^{-1} \in K.
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  3. #3
    MHF Contributor Bruno J.'s Avatar
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    Quote Originally Posted by NonCommAlg View Post
    a subset K of a group is a subgroup if and only if \forall a,b \in K: \ ab^{-1} \in K.
    And it must be nonempty
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    Quote Originally Posted by NonCommAlg View Post
    a subset K of a group is a subgroup if and only if \forall a,b \in K: \ ab^{-1} \in K.
    Thanks for this very useful criteria to prove a set is a sub-group. I always used to work with the axioms of groups.
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