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Suppose we have a semigroup S with a subgroup G≤S.

Assume there is an element s∈S that commutes with all the elements in G. Does this statement implies (or is equivalent to) another statement?

If hypothetically the elementswould have been in G, then we could have said thatswas an element of thecenterof G, but sincesis not contained in G then I suspect we can't say much more than just saying that it commutes with G, or can we?

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# Elements of semigroup commuting with subgroup

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