Linear extensions of orders invariant under abelian group actions
Colloquium Mathematicum, Tome 137 (2014) no. 1, pp. 117-125
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
Let $G$ be an abelian group acting on a set $X$, and suppose that no element of $G$ has any finite orbit of size greater than one. We show that every partial order on $X$ invariant under $G$ extends to a linear order on $X$ also invariant under $G$. We then discuss extensions to linear preorders when the orbit condition is not met, and show that for any abelian group acting on a set $X$, there is a linear preorder $\le $ on the powerset $\mathcal PX$ invariant under $G$ and such that if $A$ is a proper subset of $B$,
then $A B$ (i.e., $A\le B$ but not $B\le A$).
Keywords:
abelian group acting set suppose element has finite orbit size greater every partial order invariant under extends linear order invariant under discuss extensions linear preorders orbit condition met abelian group acting set there linear preorder powerset mathcal invariant under proper subset
Affiliations des auteurs :
Alexander R. Pruss 1
@article{10_4064_cm137_1_8,
author = {Alexander R. Pruss},
title = {Linear extensions of orders invariant under abelian group actions},
journal = {Colloquium Mathematicum},
pages = {117--125},
year = {2014},
volume = {137},
number = {1},
doi = {10.4064/cm137-1-8},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm137-1-8/}
}
Alexander R. Pruss. Linear extensions of orders invariant under abelian group actions. Colloquium Mathematicum, Tome 137 (2014) no. 1, pp. 117-125. doi: 10.4064/cm137-1-8
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