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Matthieu Romagny
Matthieu Romagny
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I apologize for this question which is obviously not research-level. I've been teaching to master students the standard generating sets of the symmetric and alternating groups and I wasn't able to give a simple, convincing example where it's useful to use the two-generating set $\{(1,2),(1,2,...,n)\}$. (I always find it annoying when we teach something and we're not able to convince the students that it's useful.) I asked a couple of colleagues and no simple answer came out -- let me stress that I'd like to find something simple enough, like a remark I could do in passing or an exercise that I could leave to the reader without cheating him/herthem. Do you know such examples ?

I apologize for this question which is obviously not research-level. I've been teaching to master students the standard generating sets of the symmetric and alternating groups and I wasn't able to give a simple, convincing example where it's useful to use the two-generating set $\{(1,2),(1,2,...,n)\}$. (I always find it annoying when we teach something and we're not able to convince the students that it's useful.) I asked a couple of colleagues and no simple answer came out -- let me stress that I'd like to find something simple enough, like a remark I could do in passing or an exercise that I could leave to the reader without cheating him/her. Do you know such examples ?

I apologize for this question which is obviously not research-level. I've been teaching to master students the standard generating sets of the symmetric and alternating groups and I wasn't able to give a simple, convincing example where it's useful to use the two-generating set $\{(1,2),(1,2,...,n)\}$. (I always find it annoying when we teach something and we're not able to convince the students that it's useful.) I asked a couple of colleagues and no simple answer came out -- let me stress that I'd like to find something simple enough, like a remark I could do in passing or an exercise that I could leave to the reader without cheating them. Do you know such examples ?

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Matthieu Romagny
Matthieu Romagny
  • 4.5k
  • 1
  • 31
  • 37

What is the standard 2-generating set of the symmetric group good for?

I apologize for this question which is obviously not research-level. I've been teaching to master students the standard generating sets of the symmetric and alternating groups and I wasn't able to give a simple, convincing example where it's useful to use the two-generating set $\{(1,2),(1,2,...,n)\}$. (I always find it annoying when we teach something and we're not able to convince the students that it's useful.) I asked a couple of colleagues and no simple answer came out -- let me stress that I'd like to find something simple enough, like a remark I could do in passing or an exercise that I could leave to the reader without cheating him/her. Do you know such examples ?