Search results for " Induced"
showing 10 items of 461 documents
The minimal number of characters over a normal p-subgroup
2007
Abstract If N is a normal p-subgroup of a finite group G and θ ∈ Irr ( N ) is a G-invariant irreducible character of N, then the number | Irr ( G | θ ) | of irreducible characters of G over θ is always greater than or equal to the number k p ′ ( G / N ) of conjugacy classes of G / N consisting of p ′ -elements. In this paper, we investigate when there is equality.
p-Parts of Brauer character degrees
2014
Abstract Let G be a finite group and let p be an odd prime. Under certain conditions on the p-parts of the degrees of its irreducible p-Brauer characters, we prove the solvability of G. As a consequence, we answer a question proposed by B. Huppert in 1991: If G has exactly two distinct irreducible p-Brauer character degrees, then is G solvable? We also determine the structure of non-solvable groups with exactly two irreducible 2-Brauer character degrees.
p-Brauer characters ofq-defect 0
1994
For ap-solvable groupG the number of irreducible Brauer characters ofG with a given vertexP is equal to the number of irreducible Brauer characters of the normalizer ofP with vertexP. In this paper we prove in addition that for solvable groups one can control the number of those characters whose degrees are divisible by the largest possibleq-power dividing the order of |G|.
Brauer's fixed-point-formula as a consequence of Thompson's order-formula
1991
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|.
Complex Systems: an Interdisciplinary Approach
2011
Two main peculiarities characterize complex systems: the nonlinearity and the noisy environmental interaction. The comprehension of noise role in the dynamics of nonlinear systems plays a key aspect in the efforts devoted to understand and model so-called complex systems.
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.
Simulating Terahertz Field-Induced Ferroelectricity in Quantum Paraelectric SrTiO3
2021
Recent experiments have demonstrated that light can induce a transition from the quantum paraelectric to the ferroelectric phase of SrTiO3. Here, we investigate this terahertz field-induced ferroelectric phase transition by solving the time-dependent lattice Schrödinger equation based on first-principles calculations. We find that ferroelectricity originates from a light-induced mixing between ground and first excited lattice states in the quantum paraelectric phase. In agreement with the experimental findings, our study shows that the nonoscillatory second harmonic generation signal can be evidence of ferroelectricity in SrTiO3. We reveal the microscopic details of this exotic phase transi…
Formation of self-trapped excitons through stimulated recombination of radiation-induced primary defects in alkali halides
1998
Abstract A self-trapped exciton formation through photostimulated recombination of an F and an H center — the exciton-created primary defect pair, is proposed and experimentally examined in alkali halides at low temperatures.