Abstract
We are now going to discuss finite actions G X,where X is a poset and where G respects the order: x < x′ ⇒ gx < gx′. Thus G acts as a group of automorphisms on (X, ≤). This yields generalizations of several notions introduced in the preceding chapter and it gives further insight. We shall also consider actions that respect the multiplication of a semigroup. Hence in particular lattice actions are considered as well as groups of automorphisms of partial orders, semigroups or other algebraic structures.
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© 1999 Springer-Verlag Berlin Heidelberg
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Kerber, A. (1999). Poset and Semigroup Actions. In: Applied Finite Group Actions. Algorithms and Combinatorics, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11167-3_6
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DOI: https://doi.org/10.1007/978-3-662-11167-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08522-2
Online ISBN: 978-3-662-11167-3
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