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Thread: Group Axioms Help

  1. #1
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    Group Axioms Help

    Hi all

    If G is a group with identity e and if A and B and subgroups of G then A*B is a subgroup of G*G.

    How do I use this to show that if A and B are two normal subgroups of G, then A*B is a normal subgroup of G*G?

    Also, if H is the subset H={(g,g):gEG} how do i show that H is a subgroup of G*G?

    Thanks again - and sorry for the previous posts around groups and geometry (not my strongest subjects)
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  2. #2
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    Quote Originally Posted by moolimanj View Post
    Hi all

    If G is a group with identity e and if A and B and subgroups of G then A*B is a subgroup of G*G.
    $\displaystyle GG=G$ thus $\displaystyle AB$ being a subgroup of $\displaystyle GG$ means $\displaystyle AB$ is subgroup of $\displaystyle G$. But that is not true. If one of $\displaystyle A,B$ is normal then it is true. In general it is not.
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