Elements of semigroup commuting with subgroup

  • Thread starter mnb96
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  • #1
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Main Question or Discussion Point

Hello,

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 element s would have been in G, then we could have said that s was an element of the center of G, but since s is 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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  • #3
WWGD
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And the term extends to subsets in general, not just to subgroups.
 
  • #4
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Thanks a lot for your answers, especially for pointing out the centralizer.
 
  • #5
WWGD
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Thanks a lot for your answers, especially for pointing out the centralizer.
I am thinking of starting an " insight" pointing out the difference between science fiction terms and abstract algebra ones. Phaser: Algebra or Sci-Fi?
 

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