# A question of order of the product of two elements

1. Mar 25, 2009

### rulin

Let $X = \{1,2,\cdots, p\}$ with $p$ prime, and $Y = \{1,2,\cdots,t,i_1,i_2,\cdots,i_{p - t}\}$ with $1\leq t\leq p - 1$ and $i_j\not\in X$ for $1\leq j\leq p - t$. Supose that $a$ and $b$ are both $p$-rotation in $X$ and $Y$, respectively. Whether or not $p$ don't divide the order of $ab$?

Last edited by a moderator: Mar 25, 2009
2. Mar 25, 2009

### confinement

Instead of dollar signs, use [ itex ][ /itex ]