Search results for "Number"

showing 10 items of 3939 documents

On the Navarro–Willems conjecture for blocks of finite groups

2007

Abstract We prove that a set of characters of a finite group can only be the set of characters for principal blocks of the group at two different primes when the primes do not divide the group order. This confirms a conjecture of Navarro and Willems in the case of principal blocks.

CombinatoricsSet (abstract data type)Discrete mathematicsFinite groupAlgebra and Number TheoryConjectureGroup (mathematics)Group orderMathematicsJournal of Pure and Applied Algebra
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ARITHMETICAL QUESTIONS IN π-SEPARABLE GROUPS

2005

If G is a finite π-separable group, π a set of primes und X is a π-suhgroup of G, let vπ(G, X) be the number of Hall π-suhgroups of G containing X. If K is a subgroup of G containing X, we prove that vπ(K,X) divides vπ(G).

CombinatoricsSet (abstract data type)Hall subgroupPure mathematicsNilpotentAlgebra and Number TheorySubgroupGroup (mathematics)Arithmetic functionMathematicsSeparable spaceCommunications in Algebra
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Basic Definitions and Facts

2001

Symbol is treated here as a primitive entity as point or line in geometry. Let Con = {f α : α < β} be a well-ordered set of symbols called a language type. β is an ordinal number. The elements of the above set are called connectives. To each connective f α a natural number α(α) ∈ w called the rank of f α or the arity of f α is assigned. The arity α(α) defines the number of arguments of f α . Thus we speak of nullary, unary, or binary connectives, etc. In the sequel Con is assumed to be fixed but arbitrary.

CombinatoricsSet (abstract data type)Unary operationSymbol (programming)Binary numberOrdinal numberNatural numberRank (differential topology)ArityMathematics
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Y-proper graded cocharacters and codimensions of upper triangular matrices of size 2, 3, 4

2012

Abstract Let F be a field of characteristic 0. We consider the upper triangular matrices with entries in F of size 2, 3 and 4 endowed with the grading induced by that of Vasilovsky. In this paper we give explicit computation for the multiplicities of the Y -proper graded cocharacters and codimensions of these algebras.

CombinatoricsSettore MAT/02 - AlgebraAlgebra and Number TheoryMathematics::Commutative AlgebraGraded identitiesComputationPolynomial identities graded identitiesTriangular matrixPolynomial identitiesMathematicsJournal of Algebra
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Transitive permutation groups in which all derangements are involutions

2006

AbstractLet G be a transitive permutation group in which all derangements are involutions. We prove that G is either an elementary abelian 2-group or is a Frobenius group having an elementary abelian 2-group as kernel. We also consider the analogous problem for abstract groups, and we classify groups G with a proper subgroup H such that every element of G not conjugate to an element of H is an involution.

CombinatoricsSubgroupAlgebra and Number TheorySymmetric groupPrimitive permutation groupElementary abelian groupAbelian groupFrobenius groupCyclic permutationMathematicsNon-abelian groupJournal of Pure and Applied Algebra
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On the divisor class group of double solids

1999

For a double solid V→ℙ3> branched over a surface B⊂ℙ3(ℂ) with only ordinary nodes as singularities, we give a set of generators of the divisor class group \(\) in terms of contact surfaces of B with only superisolated singularities in the nodes of B. As an application we give a condition when H* (˜V , ℤ) has no 2-torsion. All possible cases are listed if B is a quartic. Furthermore we give a new lower bound for the dimension of the code of B.

CombinatoricsSurface (mathematics)Number theoryDivisor summatory functionGroup (mathematics)DivisorGeneral MathematicsAlgebraic geometryUpper and lower boundsZero divisorMathematicsmanuscripta mathematica
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Groups whose real irreducible characters have degrees coprime to p

2012

Abstract In this paper we study groups for which every real irreducible character has degree not divisible by some given odd prime p .

CombinatoricsSylow p-subgroupStudy groupsCharacter (mathematics)Algebra and Number TheoryReal characterCoprime integersDegree (graph theory)Irreducible elementItô theoremPrime (order theory)MathematicsJournal of Algebra
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Imprimitive groups highly transitive on blocks

2004

We classify imprimitive groups acting highly transitively on blocks and satisfying conditions common in geometry. They can be realized as suitable subgroups of twisted wreath products.

CombinatoricsTransitive relationAlgebra and Number TheoryFlag-transitiveSocleMathematicsJournal of Group Theory
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Games without repetitions on graphs with vertex disjoint cycles

1997

Games without repetitions on graphs with vertex disjoint cycles are considered. We show that the problem finding of the game partition in this class reduces to this problem for trees. A method of finding of the game partition for trees have been given in [2].

CombinatoricsVertex (graph theory)Discrete mathematicsComputer Science::Computer Science and Game TheoryGeneral MathematicsProblem findingComputingMilieux_PERSONALCOMPUTINGPartition (number theory)Disjoint setsMathematicsofComputing_DISCRETEMATHEMATICSMathematicsArchiv der Mathematik
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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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