Search results for "Finite group"

showing 10 items of 205 documents

On 𝓕-subnormal subgroups and Frattini-like subgroups of a finite group

1994

Throughout the paper we consider only finite groups.J. C. Beidleman and H. Smith [3] have proposed the following question: “If G is a group and Ha subnormal subgroup of G containing Φ(G), the Frattini subgroup of G, such that H/Φ(G)is supersoluble, is H necessarily supersoluble? “In this paper, we give not only an affirmative answer to this question but also we see that the above result still holds if supersoluble is replaced by any saturated formation containing the class of all nilpotent groups.

CombinatoricsSubnormal subgroupNilpotentClass (set theory)Finite groupGroup (mathematics)Locally finite groupGeneral MathematicsFrattini subgroupSporadic groupMathematicsGlasgow Mathematical Journal
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The number of lifts of a Brauer character with a normal vertex

2011

AbstractIn this paper we examine the behavior of lifts of Brauer characters in p-solvable groups. In the main result, we show that if φ∈IBr(G) has a normal vertex Q and either p is odd or Q is abelian, then the number of lifts of φ is at most |Q:Q′|. As a corollary, we prove that if φ∈IBr(G) has an abelian vertex subgroup Q, then the number of lifts of φ in Irr(G) is at most |Q|.

CombinatoricsVertex (graph theory)LiftsAlgebra and Number TheoryBrauer's theorem on induced charactersCorollarySolvable groupAbelian groupFinite groupsSolvable groupsBrauer charactersMathematicsJournal of Algebra
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Sufficient conditions for supersolubility of finite groups

1998

Abstract In this paper sufficient conditions for the supersolubility of finite groups are given under the assumption that the maximal subgroups of Sylow subgroups of the group and the maximal subgroups of Sylow subgroups of the Fitting subgroup are well-situated in the group. That will improve earlier results of Srinivasan [7], Asaad et al. [1] and Ballester-Bolinches [2].

Combinatoricsp-groupMathematics::Group TheoryMaximal subgroupAlgebra and Number TheoryGroup (mathematics)Locally finite groupSylow theoremsOmega and agemo subgroupIndex of a subgroupFitting subgroupMathematicsJournal of Pure and Applied Algebra
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ON A PERMUTABILITY PROPERTY OF SUBGROUPS OF FINITE SOLUBLE GROUPS

2010

The structure and embedding of subgroups permuting with the system normalizers of a finite soluble group are studied in the paper. It is also proved that the class of all finite soluble groups in which every subnormal subgroup permutes with the Sylow subgroups is properly contained in the class of all soluble groups whose subnormal subgroups permute with the system normalizers while this latter is properly contained in the class of all supersoluble groups.

Combinatoricsp-groupSubnormal subgroupMathematics::Group TheoryFinite groupGroup (mathematics)Locally finite groupApplied MathematicsGeneral MathematicsSylow theoremsOmega and agemo subgroupComponent (group theory)MathematicsCommunications in Contemporary Mathematics
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Sylow permutable subnormal subgroups of finite groups

2002

[EN] An extension of the well-known Frobenius criterion of p-nilpotence in groups with modular Sylow p-subgroups is proved in the paper. This result is useful to get information about the classes of groups in which every subnormal subgroup is permutable and Sylow permutable.

Complement (group theory)Finite groupAlgebra and Number TheorySylow theoremsGrups Teoria deExtension (predicate logic)CombinatoricsSubnormal subgroupMathematics::Group TheoryLocally finite groupPermutable subgroupComponent (group theory)ÀlgebraPermutable primeFinite groupMATEMATICA APLICADASubnormal subgroupMathematics
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Rational irreducible characters and rational conjugacy classes in finite groups

2007

We prove that a finite group G G has two rational-valued irreducible characters if and only if it has two rational conjugacy classes, and determine the structure of any such group. Along the way we also prove a conjecture of Gow stating that any finite group of even order has a non-trivial rational-valued irreducible character of odd degree.

Computer Science::Machine LearningFinite groupApplied MathematicsGeneral MathematicsIrreducible elementComputer Science::Digital LibrariesIrreducible fractionCombinatoricsStatistics::Machine LearningConjugacy classCharacter (mathematics)Character tableComputer Science::Mathematical SoftwareOrder (group theory)Character groupMathematicsTransactions of the American Mathematical Society
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Complex group algebras of finite groups: Brauer’s Problem 1

2005

Brauer’s Problem 1 asks the following: what are the possible complex group algebras of finite groups? It seems that with the present knowledge of representation theory it is not possible to settle this question. The goal of this paper is to announce a partial solution to this problem. We conjecture that if the complex group algebra of a finite group does not have more than a fixed number m m of isomorphic summands, then its dimension is bounded in terms of m m . We prove that this is true for every finite group if it is true for the symmetric groups.

Computer Science::Machine LearningModular representation theoryPure mathematicsFinite groupBrauer's theorem on induced charactersGroup (mathematics)General MathematicsMathematicsofComputing_GENERALComputer Science::Digital LibrariesRepresentation theoryCombinatoricsStatistics::Machine LearningGroup of Lie typeSymmetric groupComputer Science::Mathematical SoftwareComputer Science::Programming LanguagesBrauer groupMathematicsElectronic Research Announcements of the American Mathematical Society
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Some subgroup embeddings in finite groups: A mini review

2015

[EN] In this survey paper several subgroup embedding properties related to some types of permutability are introduced and studied. ÂŞ 2014 Production and hosting by Elsevier B.V. on behalf of Cairo University

Computer scienceMini Reviewmacromolecular substancesS-permutabilityMini reviewMathematics::Group TheoryComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONPermutabilityPrimitive subgroupAlgebra over a fieldFinite grouplcsh:Science (General)GeneralFinite grouplcsh:R5-920MultidisciplinaryMathematics::Combinatoricsmusculoskeletal neural and ocular physiologyAlgebranervous systemEmbeddingQuasipermutable subgrouplcsh:Medicine (General)MATEMATICA APLICADAAlgorithmSemipermutabilityMathematicsofComputing_DISCRETEMATHEMATICSlcsh:Q1-390Journal of Advanced Research
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Character Tables and Sylow Subgroups Revisited

2018

Suppose that G is a finite group. A classical and difficult problem is to determine how much the character table knows about the local structure of G and vice versa.

Difficult problemPure mathematicsFinite group010102 general mathematicsSylow theorems01 natural sciencesLocal structureConjugacy classCharacter table0103 physical sciences010307 mathematical physics0101 mathematicsVersaMathematics
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Some results concerning simple locally finite groups of 1-type

2005

AbstractIn this paper several aspects of infinite simple locally finite groups of 1-type are considered. In the first part, the classes of diagonal limits of finite alternating groups, of diagonal limits of finite direct products of alternating groups, and of absolutely simple groups of 1-type are distinguished from each other. In the second part, inductive systems of representations over fields of characteristic zero (which are known to correspond to ideals in the group algebra) are studied in general for groups of 1-type. The roles of primitive respectively imprimitive representations in inductive systems are investigated. Moreover it is shown that in any proper inductive system the depth…

Discrete mathematicsAlgebra and Number TheoryProfinite groupGroup ringsGroup (mathematics)Inductive systemsSimple groupsCovering groups of the alternating and symmetric groupsLocally finite groupsGroup of Lie typeSymmetric groupSimple groupClassification of finite simple groupsGroup theoryMathematicsJournal of Algebra
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