Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let G be a topological group and a be an element of order 2 in G. Further suppose the element a does not belong to center of G. Then is it true that only homeomorphism f of G such that $f(ax)=f(x)a$ for all x in G is $f(x)=x^{-1}$.

share|cite|improve this question
No; the simplest counterexample is $S_{3}$ with the discrete topology. –  Sam Nolen Sep 4 '11 at 4:36

1 Answer 1

The answer is no. Take $H$ any topological group, $H'$ another topological group having a noncentral element $a'$ of order 2, $G=H\times H'$, $a=1_H\times a'$ and $f=h\times inv_{H'}$ where $h$ is any anti-automorphism of $H$ and $inv_{h'}$ is the map $h'\mapsto h'^{-1},h'\in H'$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.