Search results for "Normal"

Large characteristically simple sections of finite groups

2021

In this paper we prove that if G is a group for which there are k non-Frattini chief factors isomorphic to a characteristically simple group A, then G has a normal section C/R that is the direct product of k minimal normal subgroups of G/R isomorphic to A. This is a significant extension of the notion of crown for isomorphic chief factors.

Characterizations of Schunck Classes of Finite Soluble Groups

1998

All groups considered in this paper are finite and soluble.Characterization of Schunck classes and saturated formations by meansof certain embedding properties of their associated projectors plays animportant part in the Theory of Classes of Groups.Schunck classes whose projectors are normal subgroups were studied byBlessenohl and Gaschutz. They characterize these classes as the classes

Permutable subnormal subgroups of finite groups

2009

The aim of this paper is to prove certain characterization theorems for groups in which permutability is a transitive relation, the so called PT -groups. In particular, it is shown that the finite solvable PT -groups, the finite solvable groups in which every subnormal subgroup of defect two is permutable, the finite solvable groups in which every normal subgroup is permutable sensitive, and the finite solvable groups in which conjugatepermutability and permutability coincide are all one and the same class. This follows from our main result which says that the finite modular p-groups, p a prime, are those p-groups in which every subnormal subgroup of defect two is permutable or, equivalentl…

Blocks Relative to a Normal Subgroup in π-Separable Groups

2000

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