Two elements x , y : G : 𝑥 𝑦 𝐺 x,y:G in a Group G 𝐺 G are conjugate if there is an element g : G : 𝑔 𝐺 g:G such that x = g y g − 1 𝑥 𝑔 𝑦 superscript 𝑔 1 x=gyg^{-1} .