Permutation Group

gravenewworld

say you have the alternating group An for some permutation group Sn. If you are given An and then 1 odd permutation, must you be able to generate all of Sn? I tried it for S3 and I multiplied all the even perms in S3 by only 1 element that wasn't in A3 and was able to generate all of S3. Does this hold for any n?

Galileo

Yes, that is generally true.
Note that in any group multiplication on the left by an element in the group is a bijection.
[tex]ax=b \iff x=a^{-1}b[/tex]
Use this to prove it for the general case [itex]S_n ,n\geq 2[/itex]
The case n=1 is special, since the A1=S1.

gravenewworld

Alright thanks a lot galileo. I just wanted to be sure of that fact before I brought it up in my presentation that I have to give.

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gravenewworld	Permutation Group Tweet say you have the alternating group An for some permutation group Sn. If you are given An and then 1 odd permutation, must you be able to generate all of Sn? I tried it for S3 and I multiplied all the even perms in S3 by only 1 element that wasn't in A3 and was able to generate all of S3. Does this hold for any n?

Galileo Recognitions: Homework Help Science Advisor	Yes, that is generally true. Note that in any group multiplication on the left by an element in the group is a bijection. [tex]ax=b \iff x=a^{-1}b[/tex] Use this to prove it for the general case [itex]S_n ,n\geq 2[/itex] The case n=1 is special, since the A1=S1.