I need help proving a theorem!!!

Thm: Let G be a group and let H be a subgroup of G. Define N(H)=(x
exists in G such that xHx^-1=H). Prove that N(H), called the
normalizer of H, is a subgroup of G.

The only ways I have learned to show that a group is a subgroup under
another group is using the 1-step, 2-step, or finite subgroup tests.
Am I supposed to be using one of these tests to prove this? If so, I
do not know how to use these for this proof. Can anyone possibly help
me with this???

.

Relevant Pages

  • Re: I need help proving a theorem!!!-
    ... JEMebius wrote: ... normalizer of H, ... The only ways I have learned to show that a group is a subgroup under ... another group is using the 1-step, 2-step, or finite subgroup tests. ...
    (sci.math)
  • Re: I need help proving a theorem!!!-
    ... normalizer of H, ... The only ways I have learned to show that a group is a subgroup under ... another group is using the 1-step, 2-step, or finite subgroup tests. ... Johan E. Mebius ...
    (sci.math)
  • Re: centralizer and normalizer of a cyclic subgroup
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  • Re: Group of order 720
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    ... normalizer of a Sylow 5-subgroup has 10 elements. ... are of prime order, they intersect only trivially. ... a normal Sylow 2-subgroup D. D is also normal in some subgroup of G ...
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