Search results for "finite solvable group theory"

showing 2 items of 2 documents

Injectors with a normal complement in a finite solvable group

2011

Abstract Suppose G is a finite solvable group, and H is a subgroup with a normal complement in G. We shall find necessary and sufficient conditions (some of which are related to the properties of coprime actions) for H to be an injector in G. We shall also use these criteria to find characterizations of injectors which need not have a normal complement.

AlgebraAlgebra and Number TheoryCoprime integersSolvable groupinjectorfitting setfinite solvable group theorynormal complementComplement (complexity)Mathematics
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Injectors with a central socle in a finite solvable group

2013

Abstract In response to an Open Question of Doerk and Hawkes (1992) [2, IX §4, p. 628] , we shall describe three constructions for the Z π -injectors of a finite solvable group, where Z π is the Fitting class formed by the finite solvable groups whose π -socle is central (and π is a set of prime numbers).

Class (set theory)Algebra and Number Theoryfitting classinjectorPrime numberFitting subgroupCombinatoricsSet (abstract data type)Soclecentral socleSolvable groupfinite solvable group theoryNilpotent groupMathematics
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