Uniform algebras invariant under transitive group actions

2010 ◽  
Vol 59 (2) ◽  
pp. 417-426 ◽  
Author(s):  
Alexander J. Izzo
Keyword(s):  
Group Actions ◽  
Transitive Group ◽  
Uniform Algebras

scholarly journals Transitive group actions: (im)primitivity and semiregular subgroups

2014 ◽  
Vol 41 (3) ◽  
pp. 867-885 ◽  
Author(s):  
István Kovács ◽  
Aleksander Malnič ◽  
Dragan Marušič ◽  
Štefko Miklavič
Keyword(s):  
Group Actions ◽  
Transitive Group

scholarly journals Half-arc-transitive group actions with a small number of alternets

2014 ◽  
Vol 124 ◽  
pp. 114-129 ◽  
Author(s):  
Ademir Hujdurović ◽  
Klavdija Kutnar ◽  
Dragan Marušič
Keyword(s):  
Group Actions ◽  
Transitive Group

scholarly journals Finite graphs of valency 4 and girth 4 admitting half-transitive group actions

2002 ◽  
Vol 73 (2) ◽  
pp. 155-170 ◽  
Author(s):  
Dragan Marušič ◽  
Roman Nedela
Keyword(s):  
Automorphism Group ◽  
Group Actions ◽  
Transitive Group ◽  
Transitive Graph ◽  
Finite Graphs

AbstractFinite graphs of valency 4 and girth 4 admitting ½-transitive group actions, that is, vertex- and edge- but not arc-transitive group actions, are investigated. A graph is said to be ½-transitiveif its automorphism group acts ½-transitively. There is a natural orientation of the edge set of a ½-transitive graph induced and preserved by its automorphism group. It is proved that in a finite ½-transitive graph of valency 4 and girth 4 the set of 4-cycles decomposes the edge set in such a way that either every 4-cycle is alternating or every 4-cycle is directed relative to this orientation. In the latter case vertex stabilizers are isomorphic to Z2.

scholarly journals Reconstructing a minimal topological dynamical system from a set of return times

2021 ◽  
pp. 1-17
Author(s):  
KAMIL BULINSKI ◽  
ALEXANDER FISH
Keyword(s):  
Dynamical System ◽  
Finite Groups ◽  
Homogeneous Spaces ◽  
Group Actions ◽  
Transitive Group ◽  
Topological Dynamical System ◽  
Return Times ◽  
Open Set ◽  
Minimal Dynamical System

Abstract We investigate to what extent a minimal topological dynamical system is uniquely determined by a set of return times to some open set. We show that in many situations, this is indeed the case as long as the closure of this open set has no non-trivial translational symmetries. For instance, we show that under this assumption, two Kronecker systems with the same set of return times must be isomorphic. More generally, we show that if a minimal dynamical system has a set of return times that coincides with a set of return times to some open set in a Kronecker system with translationarily asymmetric closure, then that Kronecker system must be a factor. We also study similar problems involving nilsystems and polynomial return times. We state a number of questions on whether these results extend to other homogeneous spaces and transitive group actions, some of which are already interesting for finite groups.

scholarly journals Half-transitive group actions in a compact ring

1989 ◽  
Vol 60 (2) ◽  
pp. 139-153 ◽  
Author(s):  
Jo-Ann Cohen ◽  
Kwangil Koh
Keyword(s):  
Group Actions ◽  
Transitive Group ◽  
Compact Ring
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