Let 
be a maximal torus of a group 
, then 
intersects every conjugacy
class of 
,
i.e., every element 
is conjugate to a suitable element in 
. The theorem is due to É. Cartan.
Maximal Tori Theorem
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References
Hsiang, W. Y. Lectures on Lie Groups. Singapore: World Scientific, p. 42, 2000.Referenced on Wolfram|Alpha
Maximal Tori TheoremCite this as:
Weisstein, Eric W. "Maximal Tori Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MaximalToriTheorem.html