Search results for "Order theory"
showing 10 items of 150 documents
On σ-subnormality criteria in finite groups
2022
Abstract Let σ = { σ i : i ∈ I } be a partition of the set P of all prime numbers. A subgroup H of a finite group G is called σ-subnormal in G if there is a chain of subgroups H = H 0 ⊆ H 1 ⊆ ⋯ ⊆ H n = G where, for every i = 1 , … , n , H i − 1 normal in H i or H i / C o r e H i ( H i − 1 ) is a σ j -group for some j ∈ I . In the special case that σ is the partition of P into sets containing exactly one prime each, the σ-subnormality reduces to the familiar case of subnormality. In this paper some σ-subnormality criteria for subgroups of finite groups are studied.
A Dual Version of Huppert's - Conjecture
2010
Huppert’s ρ-σ conjecture asserts that any finite group has some character degree that is divisible by “many” primes. In this note, we consider a dual version of this problem, and we prove that for any finite group there is some prime that divides “many” character degrees.
Hilbert Space Embeddings for Gelfand–Shilov and Pilipović Spaces
2017
We consider quasi-Banach spaces that lie between a Gelfand–Shilov space, or more generally, Pilipovi´c space, \(\mathcal{H}\), and its dual, \(\mathcal{H}^\prime\) . We prove that for such quasi-Banach space \(\mathcal{B}\), there are convenient Hilbert spaces, \(\mathcal{H}_{k}, k=1,2\), with normalized Hermite functions as orthonormal bases and such that \(\mathcal{B}\) lies between \(\mathcal{H}_1\; \mathrm{and}\;\mathcal{H}_2\), and the latter spaces lie between \(\mathcal{H}\; \mathrm{and}\;\mathcal{H}^\prime\).
Quasi-Modes in Higher Dimension
2019
Recall that if a(x, ξ) and b(x, ξ) are two C1-functions defined on some domain in \({\mathbf {R}}^{2n}_{x,\xi }\), then we can define the Poisson bracket to be the C0-function on the same domain given by $$\displaystyle \{ a,b\} =a^{\prime }_\xi \cdot b^{\prime }_x-a^{\prime }_x \cdot b^{\prime }_\xi =H_a(b). $$ Here \(H_a=a^{\prime }_\xi \cdot \partial _x-a^{\prime }_x\cdot \partial _\xi \) denotes the Hamilton vector field of a. The following result is due to Zworski, who obtained it via a semi-classical reduction from the above mentioned result of Hormander. A direct proof was given in Dencker et al. and here we give a variant. We will assume some familiarity with symplectic geometry.
Zu einem Satz von Isaacs �ber das Casus-Irreducibilis Ph�nomen
2000
Let \(\Omega \) be a field (of characteristic 0). A prime p is called “bose” (naughty) if \(\Omega \) contains all p-th roots of unity. In this paper the theorem is proved: Let K be an admissible subfield of \(\Omega \) (i.e. for each prime p K contains all p-th roots of unity lying in \(\Omega \)), a an algebraic element of \(\Omega /K\) which is contained in a repeated radical extension of K lying in \(\Omega \). Furthermore let the normal hull L of a over K be contained in \(\Omega \). Then all prime divisors of \(\mid L : K \mid \) are naughty (and L is a repeated radical extension of K with naughty prime exponents). This result generalises a theorem of Isaacs [1] who treats the case \(…
Restriction of characters to Sylow normalizers
2001
Suppose that G is a finite p -solvable group and let \chi \in {\rm Irr}(G) be of p^\prime -degree. In this note, we investigate when \chi remains irreducible when restricted to {\bf {N)}_{G}(P) .
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 .
ADDITIVITY FROM MULTIPLE PRIMES IN IDENTIFYING BACKWARD WRITTEN WORDS
1988
Activational theories of memory assume that activation from several sources adds up to an intersecting node. We tested this idea in one experiment where we kept constant the number of primes presented and we manipulated the number of different primes related to the target, the number of presentations of the same prime, or the same target, presented as a prime. We used a task in which the target was always a word, which appeared written backward and had to be identified. We found a strong effect of target repetition and diminished priming in the condition in which the target was repeated. We obtained additivity (greater activation) mainly in the condition in which we presented several diffe…
Effect of Prime and Target Repetition on Lexical Decision Time
1992
On a prime-target lexical decision task we manipulated the relatedness between prime and target (semantically related or unrelated), the number of repetitions (from 1 to 5), the type of the repeated stimulus (only the prime, only the target, or both), and the stimulus onset asynchrony (within a range of automatic activation from 60 to 400 msec.) to find whether semantic and repetition priming are additive (or interact), and whether there is episodic priming in an automatic, nonconscious way. Analysis showed repetition and semantic priming were additive rather than interactive. No episodic automatic priming was found. Results are discussed in terms of the predictions made from the main theo…
Automatic construction of test sets: Theoretical approach
2005
We consider the problem of automatic construction of complete test set (CTS) from program text. The completeness criterion adopted is C1, i.e., it is necessary to execute all feasible branches of program at least once on the tests of CTS. A simple programming language is introduced with the property that the values used in conditional statements are not arithmetically deformed. For this language the CTS problem is proved to be algorithmically solvable and CTS construction algorithm is obtained. Some generalizations of this language containing counters, stacks or arrays are considered where the CTS problem remains solvable. In conclusion the applications of the obtained results to CTS constr…