1 Let (G,.) be a group. Suppose that a, b €G are given such that ab=ba (Note that G need not be abelian). Prove that: {x

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1 Let G Be A Group Suppose That A B G Are Given Such That Ab Ba Note That G Need Not Be Abelian Prove That X 1 (64 KiB) Viewed 35 times

1 Let (G,.) be a group. Suppose that a, b €G are given such that ab=ba (Note that G need not be abelian). Prove that: {xe Gla.x+b=box.a} a subgroup of G Find the order of this subgroup when G = S3 α = (123), b = (1 32). is