Search results for "Transitive group"

showing 2 items of 2 documents

A class of imprimitive groups

2010

We classify imprimitive groups inducing the alternating group A4 on the set of blocks, with the inertia subgroup satisfying some very natural geometrical conditions which force the group to operate linearly.

Class (set theory)Algebra and Number Theorypermutation groups imprimitive groups sharply transitive groupsPermutation groupsGroup (mathematics)Applied Mathematicsmedia_common.quotation_subjectAlternating groupimprimitive groupsPermutation groupInertiaCombinatoricsPermutation groups; imprimitive groups; sharply transitive groupsSettore MAT/03 - GeometriaMathematicsmedia_commonsharply transitive groups
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Homogeneous three-dimensional Riemannian spaces

2020

The necessary and sufficient conditions for a three-dimensional Riemannian metric to admit a transitive group of isometries are obtained. These conditions are Intrinsic, Deductive, Explicit and ALgorithmic, and they offer an IDEAL labeling of these geometries. It is shown that the transitive action of the group naturally falls into an unfolding of some of the ten types in the Bianchi-Behr classification. Explicit conditions, depending on the Ricci tensor, are obtained that characterize all these types.

PhysicsPure mathematicsIdeal (set theory)Physics and Astronomy (miscellaneous)010308 nuclear & particles physicsGroup (mathematics)Transitive actionFOS: Physical sciencesTransitive groupGeneral Relativity and Quantum Cosmology (gr-qc)01 natural sciencesGeneral Relativity and Quantum CosmologyHomogeneous0103 physical sciencesHomogeneous spaceMetric (mathematics)Mathematics::Differential Geometry010306 general physicsRicci curvature
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