If [math]G[/math] is a finite group and [math]g,h\in G[/math] then is it true that [math]g[/math] and [math]h[/math] have the same order if and only if there exists another group [math]H[/math] containing [math]G[/math] s.t. [math]g[/math] and [math]h[/math] are conjugate in [math]H[/math]? - The Math Hub - Quora
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