Given a subgroup $\displaystyle A \subseteq G$, consider the set $\displaystyle N_G(A) = \{g \in G | gAg^{-1} = A\}$.

Prove that $\displaystyle A$ is normal if and only if $\displaystyle N_G(A) = G$.

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- Mar 2nd 2011, 07:24 PMJJMC89Given a subgroup A in G, consider the normalizer. Prove A is normal iff normalizer=G.
Given a subgroup $\displaystyle A \subseteq G$, consider the set $\displaystyle N_G(A) = \{g \in G | gAg^{-1} = A\}$.

Prove that $\displaystyle A$ is normal if and only if $\displaystyle N_G(A) = G$. - Mar 2nd 2011, 07:32 PMDrexel28
- Mar 2nd 2011, 07:36 PMJJMC89
- Mar 2nd 2011, 07:54 PMDrexel28
- Mar 2nd 2011, 08:01 PMJJMC89