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Obtaining a poset associated to a finite group

asked 4 years ago

klaaa gravatar image

updated 2 years ago

FrédéricC gravatar image

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

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answered 4 years ago

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: 4 years ago

Seen: 225 times

Last updated: Sep 13 '20