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Post Reopened by quid, Richard Kent, Qiaochu Yuan, Kevin Buzzard, Anton Geraschenko♦♦
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Question Is $ord(xy)$ independent of $ord(x)$ and $ord(y)$ in a finite grouptheory?Let r,s,t $r,s,t>1$ be positive integersgreater that 1. Show that Must there exists exist a finite group G having $G$ with elements x $x$ and y $y$ such that ord(x)=r,ord(y)=s,and ord(xy)=t. $ord(x)=r$, $ord(y)=s$, and $ord(xy)=t$? The answer is probably "yes." Is there a nice description of such a $G$? |
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Post Closed as "off topic" by Emil Jeřábek, Mariano Suárez-Alvarez, Andreas Blass, GH, Anton Geraschenko♦♦
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