I am teaching an introductory group theory course, and it has come to the inevitable proof that $A_n$ is simple for $n\geq 5.$ Now, there seem to be a number of proofs that I can find - one the "standard" one with $3$-cycles, and the others using primitivity or conjugacy class size estimation. Does anyone have a list of proofs of simplicity of $A_n$ with comments? I am sure there are a number of different ideas which could be used... In particular, any method that generalizes to some of the other finite simple groups would be of particular interest...

I am teaching an introductory group theory course, and it has come to the inevitable proof that $A_n$ is simple for $n\geq 5$. Now, there seem to be a number of proofs that I can find – one the "standard" one with $3$-cycles, and the others using primitivity or conjugacy class size estimation. Does anyone have a list of proofs of simplicity of $A_n$ with comments? I am sure there are a number of different ideas which could be used... In particular, any method that generalizes to some of the other finite simple groups would be of particular interest...

I am teaching an introductory group theory course, and it has come to the inevitable proof that $A_n$ is simple for $n\geq 5.$ Now, there seem to be a number ofproofs that I can find - one the "standard" one with $3$-cycles, and the others using primitivity or conjugacy class size estimation. Does anyone have a list of proofs of simplicity of $A_n$ with comments? I am sure there are a number of different ideas which could be used... In particular, any method that generalizes to some of the other finite simple groups would be of particular interest...

I am teaching an introductory group theory course, and it has come to the inevitable proof that $A_n$ is simple for $n\geq 5.$ Now, there seem to be a number of proofs that I can find - one the "standard" one with $3$-cycles, and the others using primitivity or conjugacy class size estimation. Does anyone have a list of proofs of simplicity of $A_n$ with comments? I am sure there are a number of different ideas which could be used... In particular, any method that generalizes to some of the other finite simple groups would be of particular interest...