# QuestionIs$ord(xy)$independentof$ord(x)$and$ord(y)$ in afinite 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 $G$?