If you find any mistakes, please make a comment! Thank you.

Finite symmetric groups of different orders are not isomorphic


Prove that if $n \neq m$ then $S_n$ and $S_m$ are not isomorphic.


Solution: We know that $|S_n| = n!$ and $|S_m| = m!$, but if $n \neq m$ then $n! \neq m!$.

Linearity

This website is supposed to help you study Linear Algebras. Please only read these solutions after thinking about the problems carefully. Do not just copy these solutions.
Close Menu