I would appreciate some advice as how to start with the following problem:
Show through induction that in every Group G, for all $a_1,a_2,a_3,..., a_n$ that: $\mathrm{ord}( a_1 \circ a_2 \circ ... \circ a_{n-1} \circ a_n) = \mathrm{ord}(a_2 \circ a_3 \cdots\circ a_{n-1} \circ a_n \circ a_1) $
Me and some friends have talked about this. if the group was abelian, or if it was said that the operation is commutative, our job would have been done. however, we are pretty lost in this and basically are stuck on the "how do we proceed" department.
I appreciate any tips.