Search results for "Subgroup"

Local Near-Rings and Triply Factorized Groups

2004

Abstract Groups G of the form G = AB = AM = BM for two subgroups A and B of G and a normal subgroup M of G with A ∩ M = B ∩ M = 1 are called triply factorized and play an important role in the theory of factorized groups. In this paper, a method to construct triply factorized groups with non-abelian M using local near-rings is introduced.

Partial characters with respect to a normal subgroup

1999

AbstractSuppose that G is a π-separable group. Let N be a normal π1-subgroup of G and let H be a Hall π-subgroup of G. In this paper, we prove that there is a canonical basis of the complex space of the class functions of G which vanish of G-conjugates ofHN. When N = 1 and π is the complement of a prime p, these bases are the projective indecomposable characters and set of irreduciblt Brauer charcters of G.

An answer to a question of Isaacs on character degree graphs

2006

Abstract Let N be a normal subgroup of a finite group G. We consider the graph Γ ( G | N ) whose vertices are the prime divisors of the degrees of the irreducible characters of G whose kernel does not contain N and two vertices are joined by an edge if the product of the two primes divides the degree of some of the characters of G whose kernel does not contain N. We prove that if Γ ( G | N ) is disconnected then G / N is solvable. This proves a strong form of a conjecture of Isaacs.

ApproximatingL 2-invariants by their finite-dimensional analogues

1994

LetX be a finite connectedCW-complex. Suppose that its fundamental group π is residually finite, i.e. there is a nested sequence ... ⊂ Г m + 1 ⊂ Г m ⊂ ... ⊂ π of in π normal subgroups of finite index whose intersection is trivial. Then we show that thep-thL 2-Betti number ofX is the limit of the sequenceb p(Xm)/[π:Г m ] whereb p(Xm) is the (ordinary)p-th Betti number of the finite covering ofX associated with Г m .

An answer to two questions of Brewster and Yeh on M-groups

2003

Let χ be a (complex) irreducible character of a finite group. Recall that χ is monomial if there exists a linear character λ ∈ Irr(H), where H is some subgroup of G, such that χ = λG. A group is an M -group if all its irreducible characters are monomial. In 1992, B. Brewster and G. Yeh [1] raised the following two questions. Question A. Let M and N be normal subgroups of a group G. Assume that (|G : M |, |G : N |) = 1 and that M and N are M -groups. Does this imply that G is an M -group? ∗Research supported by the Basque Government, the Spanish Ministerio de Ciencia y Tecnoloǵia and the University of the Basque Country

Brauer Characters Relative to a Normal Subgroup

2000

On maximal subgroups of finite groups

1991

(1991). On maximal subgroups of finite groups. Communications in Algebra: Vol. 19, No. 8, pp. 2373-2394.

Local Finite Group Theory

1982

The word local is used in finite group-theory in relation to a fixed prime p; thus properties of p-subgroups or their normalisers, for example, are regarded as local. In the case of a soluble group, then, everything is local, but an insoluble group also has global aspects. Now the local behaviour influences the global, that is, there are theorems in which the hypothesis involves only p-subgroups and their normalisers, but the conclusion involves the whole group. This chapter is an introduction to theorems of this sort.

A characteristic subgroup and kernels of Brauer characters

2005

If G is finite group and P is a Sylow p-subgroup of G, we prove that there is a unique largest normal subgroup L of G such that L ⋂ P = L ⋂ NG (P). If G is p-solvable, then L is the intersection of the kernels of the irreducible Brauer characters of G of degree not divisible by p.

On $MC$-hypercentral triply factorized groups

2007

A group G is called triply factorized in the product of two subgroups A, B and a normal subgroup K of G ,i fG = AB = AK = BK. This decomposition of G has been studied by several authors, investigating on those properties which can be carried from A, B and K to G .I t is known that if A, B and K are FC-groups and K has restrictions on the rank, then G is again an FC-group. The present paper extends this result to wider classes of FC-groups. Mathematics Subject Classification: 20F24; 20F14