New answers tagged

3 votes

An easy proof that $S(n)$ does not embed into $A(n+1)$?

Here is a short proof that follows from Rotman's material: Automorphisms of $S_m$ are all inner unless $m=2 \text{ or } 6$. It is not hard to use this to show that for $m\neq 2, 6$ subgroups of $S_m$ ...
user avatar
  • 2,132
1 vote

An easy proof that $S(n)$ does not embed into $A(n+1)$?

Using concepts that Rotman have introduced before that exercise, I think we could provide the following counterexample: if $S_2$ could be embedded in $A_3$, then in $A_3$ there would be a subgroup $H$ ...
user avatar
  • 11

Top 50 recent answers are included