Abstract Algebra: Theory and Applications · Problem 23

Permutation Groups — Thomas Judson

Mathematics — Abstract Algebra · cyclic-groups-element-orders

Problem

Let

a, b \in G

. Prove the following statements. ((a)) The order of

a

is the same as the order of

a^{-1}

. ((b)) For all

g \in G

|a| = |g^{-1}ag|

. ((c)) The order of

ab

is the same as the order of

ba