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Posted: **Tue Jul 12, 2022 12:41 pm**

: 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 G A 1 (64 KiB) Viewed 32 times

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∈G∣a⋅x⋅b=b⋅x⋅a} is a subgroup of G. Find the order of this subgroup when G=S3 a=(123),b=(132)