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Obtaining a poset associated to a finite group

asked 2020-09-12 22:41:43 +0200

klaaa gravatar image

updated 2022-06-30 21:06:45 +0200

FrédéricC gravatar image

Let $G$ be a finite group and use Cayley's theorem to embed $G$ into the symmetric group $S_n$. Is it possible via Sage to get the subposet of the strong Bruhat order (or the weak Bruhat order) on $S_n$ that has the points of $G$ inside $S_n$ with the induced poset structure?

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answered 2020-09-13 08:20:47 +0200

FrédéricC gravatar image

Like this

sage: W = SymmetricGroup(4)                                                       
sage: G = AlternatingGroup(4)                                                     
sage: Poset((G,lambda x,y : W(x).bruhat_le(W(y))))                              
Finite poset containing 12 elements
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Asked: 2020-09-12 22:41:43 +0200

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Last updated: Sep 13 '20