Group Actions on Boolean Algebras

Part of the Undergraduate Texts in Mathematics book series (UTM)


Let us begin by reviewing some facts from group theory. Suppose that X is an n-element set and that G is a group. We say that Gacts on the set X if for every element π of G we associate a permutation (also denoted π) of X, such that for all xX and π,σG we have
$$\displaystyle{\pi (\sigma (x)) = (\pi \sigma )(x).}$$
Thus [why?] an action of G on X is the same as a homomorphism


Quotient Poset Symmetric Chain Decomposition Edge Reconstruction Conjecture Sperner Property Vertex Permutation 
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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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