Linear extensions of orders invariant under abelian group actions

Alexander R. Pruss. "Linear extensions of orders invariant under abelian group actions." Colloquium Mathematicae 137.1 (2014): 117-125. <http://eudml.org/doc/283800>.

@article{AlexanderR2014,
abstract = {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 ≤ on the powerset 𝓟X invariant under G and such that if A is a proper subset of B, then A < B (i.e., A ≤ B but not B ≤ A).},
author = {Alexander R. Pruss},
journal = {Colloquium Mathematicae},
keywords = {linear orders; extensions of orders; Abelian group actions; linear preorders},
language = {eng},
number = {1},
pages = {117-125},
title = {Linear extensions of orders invariant under abelian group actions},
url = {http://eudml.org/doc/283800},
volume = {137},
year = {2014},
}

TY - JOUR
AU - Alexander R. Pruss
TI - Linear extensions of orders invariant under abelian group actions
JO - Colloquium Mathematicae
PY - 2014
VL - 137
IS - 1
SP - 117
EP - 125
AB - 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 ≤ on the powerset 𝓟X invariant under G and such that if A is a proper subset of B, then A < B (i.e., A ≤ B but not B ≤ A).
LA - eng
KW - linear orders; extensions of orders; Abelian group actions; linear preorders
UR - http://eudml.org/doc/283800
ER -