Determine order of ⟨123452354⟩.I'm asked to prove that the order of H=⟨123452354⟩ is 20, in an Algebra exercise 2nd year maths.What I have achieved is that 20||H|and|H∣=20,120 since H can't be the alternating group and there are no subgroups of order 40 in S5. But I don't know how to prove H≠S5.

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Determine order of ⟨123452354⟩.I&#039;m asked to prove that the order of H=⟨123452354⟩ is 20, in an Algebra exercise 2nd year maths.What I have achieved is that 20||H|and|H∣=20,120 since H can&#039;t be the alternating group and there are no subgroups of order 40 in S5. But I don&#039;t know how to prove H≠S5.

Biscatta9rz · Accepted Answer

Consider the integers modulo 5. Let α be the operation α:x→x+1. Let β be the operation β:x→2x.  Then α,β generate all affine automorphisms of Z5Z, which has size 20:  x→ax+b,  with a∈{1,2,3,4} and b∈{0,1,2,3,4,5}.

Determine order of \langle(12345), (2354) \rangle. I'm asked to prove that the order of PS

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