Mistake in a study book?
Yes, there really is mistake in a text of exercise.
The even simplier counterexample, submitted by jspecter: $(1)\not=(12)$, but $(1)^2=(12)^2$
For cycles of odd length, as Jyrki Lahtonen noted, the exercise claim holds.
Yes, there really is mistake in a text of exercise.
The even simplier counterexample, submitted by jspecter: $(1)\not=(12)$, but $(1)^2=(12)^2$
For cycles of odd length, as Jyrki Lahtonen noted, the exercise claim holds.