Skip to main content
1 of 4
C.S.
  • 4.8k
  • 7
  • 41
  • 49

Group cannot be the Union of Conjugates

I have seen this problem, that if $G$ is a finite group and $H$ is a proper subgroup of $G$ with finite index then $ G \neq \bigcup\limits_{g \in G} ghg^{-1}$. Does this remain true for the infinite case also.

C.S.
  • 4.8k
  • 7
  • 41
  • 49