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International Journal of Algebra and Computation, 2013
We give a general structure theory for reconstructing non-trivial group actions on sets without any further assumptions on the group, the action, or the set on which the group acts. Using certain "local data" [Formula: see text] from the action we build a group [Formula: see text] of the data and a space [Formula: see text] with an action of [Formula ...
Lisa Carbone, Eliyahu Rips
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We give a general structure theory for reconstructing non-trivial group actions on sets without any further assumptions on the group, the action, or the set on which the group acts. Using certain "local data" [Formula: see text] from the action we build a group [Formula: see text] of the data and a space [Formula: see text] with an action of [Formula ...
Lisa Carbone, Eliyahu Rips
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International Journal of Algebra and Computation, 2004
A partial action of a group G on a set X is a weakening of the usual notion of a group action: the function G×X→X that defines a group action is replaced by a partial function; in addition, the existence of g·(h·x) implies the existence of (gh)·x, but not necessarily conversely.
Johannes Kellendonk, Mark V. Lawson
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A partial action of a group G on a set X is a weakening of the usual notion of a group action: the function G×X→X that defines a group action is replaced by a partial function; in addition, the existence of g·(h·x) implies the existence of (gh)·x, but not necessarily conversely.
Johannes Kellendonk, Mark V. Lawson
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2015
In this paper, we introduce a logic to reason about group actions for groups that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show.
Porello, Daniele
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In this paper, we introduce a logic to reason about group actions for groups that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show.
Porello, Daniele
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2020
This chapter provides the foundations for deriving a class of manifolds known as homogeneous spaces. It begins with a short review of group theory, introduces the concept of a group acting on a set, and defines the Grassmannians and Stiefel manifolds as homogenous manifolds arising from group actions of Lie groups. The last section provides an overview
Jean Gallier, Jocelyn Quaintance
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This chapter provides the foundations for deriving a class of manifolds known as homogeneous spaces. It begins with a short review of group theory, introduces the concept of a group acting on a set, and defines the Grassmannians and Stiefel manifolds as homogenous manifolds arising from group actions of Lie groups. The last section provides an overview
Jean Gallier, Jocelyn Quaintance
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Actions of abelian groups on groups
Journal of Group Theory, 2007Let G be a group and A a finitely generated abelian subgroup of Aut(G). If G is the union of a finitely many A-orbits then G is finite.
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