Talk:Schützenberger group

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Latest comment: 11 years ago by Jsedenka

left and right Schutzenberger groups are isomorphic or antiisomorphic?

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"In fact, there are two Schutzenberger groups associated with a given H-class and each is antiisomorphic to the other." I supposte the "two" Schutzenberger groups means the left and right Schutzenberger group for H. Let   be the left one,   the right one.

Then, only this natural isomorphism   comes to my mind:  . If  , then  , so   meaning that  .

Under this mapping, left and right Schutzenberger groups are isomorphic, not antiisomorphic. Moreover, the isomorphism can be used for proving that all Green H-classes in a regular D-class are isomorphic groups, while the antiisomorphism is not directly required. So, I think the article introduction is somewhat confusing. Could someone describe the antiisomorphism explicitly in the article, or add a direct reference? Or is the antiisomorphism just  ? — Preceding unsigned comment added by Jsedenka (talkcontribs) 12:28, 9 February 2013 (UTC)Reply