Conjugates Generating a regular subgroup
This trouble is extracted from I.N. Herstein
If $G$ is a team and also $a \in G$ if of limited order and also has just a limited variety of conjugates in $G$, confirm that these conjugates of $a$ create a limited regular subgroup of $G$.
I would love to see a remedy for this as well as additionally I would love to recognize whether the conjugates constantly create a regular subgroup.