0

Let $G$ be the non-abelian finite group whose order is divisible by $3$. Prove that exist a left invariant but not right invariant metric on $G$.

Mikasa
  • 67,374
Vanthuan
  • 141

1 Answers1

3

It seems that answering another your quention about Metric on a group, I have proved that $|G|$ is a power of 2 (see the line after Lemma 1).

Community
  • 1
Alex Ravsky
  • 90,434
  • 1
    It's best if you put the link in this answer (not just the comment), summarize the result in the link (i.e. the line after Lemma 1 seems to be the relevant point), and say why it implies the desired result asked about here. – Henry T. Horton Apr 24 '13 at 02:36