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A practical method for enumerating cosets of a finite abstract group
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Geometric Group TheoryRepresentation TheoryGroup Theory (Counseling Psychology)Finite Abstract GroupLinear GroupsAbstract DefinitionGroup Theory (Abstract Algebra)Frattini SubgroupEducationOrdered GroupHigh OrderPractical MethodGroup RepresentationNilpotent GroupGroup StructureAbstract DefinitionsCombinatorial Group Theory
An important problem in finite-group theory is the determination of an abstract definition for a given group , that is, a set of relations between k generating operations S 1 , …., S k of , such that every other relation between S 1 , …., S k is an algebraic consequence of (1). The number of groups for which abstract definitions are actually known is relatively small, but a remarkable feature of the results already obtained is the extreme simplicity of the relations (1) in the case of several groups of quite high order. This fact constitutes an additional incentive to the search for abstract definitions, and many elegant results have doubtless yet to be discovered.