1) Let G be a group and let a E G such that |a= n. Prove the following: [a] = |xax-'], for any x E G. ii) |am| = where (

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1 Let G Be A Group And Let A E G Such That A N Prove The Following A Xax For Any X E G Ii Am Where 1 (44.98 KiB) Viewed 14 times

1) Let G be a group and let a E G such that |a= n. Prove the following: [a] = |xax-'], for any x E G. ii) |am| = where (n, m) denotes the greatest common divisor (n.m) 开 between n and m. iii) If a is the only element of G with order n, show that a € C(G) = {b E G: bx = xb, for all x E G}