Solution
= Solution
\b[No.] In any <group> choose a nonidentity $x$ and put $y=x^{-1}$. They commute, but $xy=e$ has order one rather than $o(x)o(y)$.
= Solution
\b[No.] In any <group> choose a nonidentity $x$ and put $y=x^{-1}$. They commute, but $xy=e$ has order one rather than $o(x)o(y)$.