S4 is generated by (12) and (1234). Prove that (13) and (1234) generate a copy of...

 

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S4 is generated by (12) and (1234). Prove that (13) and (1234) generate a copy of Dg in S4. Prove that every subgroup of S4 of order 8 is conjugate to ((13), (1234)). Prove there are exactly 3 such subgroups. For all n 3 that Sn contains a copy of the dihedral group D2n, and find generators for it. prove S4 is generated by (12) and (1234). Prove that (13) and (1234) generate a copy of Dg in S4. Prove that every subgroup of S4 of order 8 is conjugate to ((13), (1234)). Prove there are exactly 3 such subgroups. For all n 3 that Sn contains a copy of the dihedral group D2n, and find generators for it. prove

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To prove that the elements 13 and 1234 generate a copy of D in S we need to show two things 1 The elements 13 and 1234 satisfy the defining relations ... View the full answer