Practice Problem 30 Let (G, .) be a group. Suppose that a, be G are given such that ab=ba. (Note that G need not be abel

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Practice Problem 30 Let G Be A Group Suppose That A Be G Are Given Such That Ab Ba Note That G Need Not Be Abel 1 (97.18 KiB) Viewed 22 times

Practice Problem 30 Let (G, .) be a group. Suppose that a, be G are given such that ab=ba. (Note that G need not be abelian). Prove that: {xe Gla⋅x · b = b⋅x.a} is a subgroup of G. Find the order of this subgroup when G=S3. a= (1 2 3), b= (132)