Conjugates Generating a regular subgroup

This trouble is extracted from I.N. Herstein

Problem :
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.

2019-05-09 11:40:03
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Answers: 1

This called Dicman's lemma and also is 14.5.7 on web page 425 (1st ed) or page 442 (2nd ed) of Robinson's Course in the Theory of Groups.

2019-05-10 09:48:16