Using the associativity
PSK(a^-1ba)^n={(a^-1ba)(a^-1ba)...(a^-1ba)} n times
=a^-1b(aa^-1)b(aa^-1)...b(aa^-1)ba
=a^-1bebe...beba
=a^-1b^naZSK

Question

asked 2021-05-08

Use the factorization theorem to prove that x−c is a factor of \(x^{n}−c^{n}\) for any positive integer n.

asked 2020-11-07

For any elements a and to from a group and any integer n, prove that \(\displaystyle{\left({a}^{{-{{1}}}}{b}{a}\right)}^{{n}}={a}^{{-{{1}}}}{b}^{{n}}{a}\).

asked 2020-11-08

The proof of the given statement.

asked 2021-01-05