Search results for "REPRESENTATION"
showing 10 items of 1710 documents
Groups with few $p'$-character degrees
2019
Abstract We prove a variation of Thompson's Theorem. Namely, if the first column of the character table of a finite group G contains only two distinct values not divisible by a given prime number p > 3 , then O p p ′ p p ′ ( G ) = 1 . This is done by using the classification of finite simple groups.
A characterisation of nilpotent blocks
2015
Let $B$ be a $p$-block of a finite group, and set $m=$ $\sum \chi(1)^2$, the sum taken over all height zero characters of $B$. Motivated by a result of M. Isaacs characterising $p$-nilpotent finite groups in terms of character degrees, we show that $B$ is nilpotent if and only if the exact power of $p$ dividing $m$ is equal to the $p$-part of $|G:P|^2|P:R|$, where $P$ is a defect group of $B$ and where $R$ is the focal subgroup of $P$ with respect to a fusion system $\CF$ of $B$ on $P$. The proof involves the hyperfocal subalgebra $D$ of a source algebra of $B$. We conjecture that all ordinary irreducible characters of $D$ have degree prime to $p$ if and only if the $\CF$-hyperfocal subgrou…
New Refinements of the McKay Conjecture for Arbitrary Finite Groups
2004
Let $G$ be an arbitrary finite group and fix a prime number $p$. The McKay conjecture asserts that $G$ and the normalizer in $G$ of a Sylow $p$-subgroup have equal numbers of irreducible characters with degrees not divisible by $p$. The Alperin-McKay conjecture is a version of this as applied to individual Brauer $p$-blocks of $G$. We offer evidence that perhaps much stronger forms of both of these conjectures are true.
Almost polynomial growth: Classifying varieties of graded algebras
2015
Let G be a finite group, V a variety of associative G-graded algebras and c (V), n = 1, 2, …, its sequence of graded codimensions. It was recently shown by Valenti that such a sequence is polynomially bounded if and only if V does not contain a finite list of G-graded algebras. The list consists of group algebras of groups of order a prime number, the infinite-dimensional Grassmann algebra and the algebra of 2 × 2 upper triangular matrices with suitable gradings. Such algebras generate the only varieties of G-graded algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety is polynomially bounded. In this paper we completely classify all sub…
On irreducible products of characters
2021
Abstract We study the problem when the product of two non-linear Galois conjugate characters of a finite group is irreducible. We also prove new results on irreducible tensor products of cross-characteristic Brauer characters of quasisimple groups of Lie type.
Irreducible restriction and zeros of characters
2000
Let G be a finite group, let N be normal in G and suppose that X is an irreducible complex character of G. Then XN is not irreducible if and only if X vanishes on some coset of N in G.
Finite groups with real-valued irreducible characters of prime degree
2008
Abstract In this paper we describe the structure of finite groups whose real-valued nonlinear irreducible characters have all prime degree. The more general situation in which the real-valued irreducible characters of a finite group have all squarefree degree is also considered.
Research of a Cellular Automaton Simulating Logic Gates by Evolutionary Algorithms
2003
This paper presents a method of using genetic programming to seek new cellular automata that perform computational tasks. Two genetic algorithms are used : the first one discovers a rule supporting gliders and the second one modifies this rule in such a way that some components appear allowing it to simulate logic gates. The results show that the genetic programming is a promising tool for the search of cellular automata with specific behaviors, and thus can prove to be decisive for discovering new automata supporting universal computation.
When the arts inspire businesses: Museums as a heritage redefinition tool of brands
2018
International audience; While the literature has mainly considered brand museums as communication tools or complex retail environments, this article analyses them through a heritage framework and suggests that brands can use heritage technologies of the arts for their own purposes. The case study of the brand museum of the Laughing Cow highlights the heritage technologies the brand uses to endorse two heritage roles: an inter-generational memory role based on the transmission of the brand's history and a community representation role through spaces and objects. As a consequence, this research sheds light on how brands can come to be accepted as heritage objects. By using heritage technologi…
Modeling Requirements for Future CASE
1995
In this paper we discuss some requirements for future CASE Computer Aided Software/Systems Engineering environments. These requirements include increased modifiability and flexibility as well as support for process and agent models. We claim that they can only be addressed by developing more powerful representation and modeling techniques. As a possible basis for modeling various techniques, we outline a general information architecture for a future CASE environment. In addition, we propose primitive types for specifying techniques, the development process, and agent models, and use these types for modeling an example methodology and examine how the requirements are or can be supported in o…