Search results for "maximal"
showing 10 items of 239 documents
On the Deskins index complex of a maximal subgroup of a finite group
1999
AbstractLet M be a maximal subgroup of a finite group G. A subgroup C of G is said to be a completion of M in G if C is not contained in M while every proper subgroup of C which is normal in G is contained in M. The set, I(M), of all completions of M is called the index complex of M in G. Set P(M) = {C ϵ I(M) ¦ C} is maximal in I(M) and G = CM. The purpose of this note is to prove: A finite group G is solvable if and only if, for each maximal subgroup M of G, P(M) contains element C with CK(C) nilpotent.
On the normal index of maximal subgroups in finite groups
1990
AbstractFor a maximal subgroup M of a finite group G, the normal index of M is the order of a chief factor H/K where H is minimal in the set of normal supplements of M in G. We use the primitive permutation representations of a finite group G and the normal index of its maximal subgroups to obtain results about the influence of the set of maximal subgroups in the structure of G.
OnF-Subnormal Subgroups andF-Residuals of Finite Soluble Groups
1996
All groups that we consider are finite and soluble. Recall that a formation is a class of groups which is closed under homomorphic images and subdirect products. Hence, if F is a formation and G is a group which is a direct product of the subgroups A and B, then G is in F if and only if A and B lie in F. More generally, Doerk and w x Hawkes 4, IV, 1.18 proved that if G is a group such that G s A = B, then G s A = B , where G is the F-residual of G, that is, the smallest normal subgroup of G with quotient in F. The main purpose of this paper is the development of this result by means of the concept of F-subnormal subgroup. Suppose that F is a saturated formation. A maximal subgroup M of a Ž …
The Variation of the Fractional Maximal Function of a Radial Function
2017
Abstract In this article, we study the regularity of the non-centered fractional maximal operator $M_{\beta}$. As the main result, we prove that there exists $C(n,\beta)$ such that if $q=n/(n-\beta)$ and $f$ is radial function, then $\|DM_{\beta}f\|_{L^{q}({\mathbb{R}^n})}\leq C(n,\beta)\|Df\|_{L^{1}({\mathbb{R}^n})}$. The corresponding result was previously known only if $n=1$ or $\beta=0$. Our proofs are almost free from one-dimensional arguments. Therefore, we believe that the new approach may be very useful when trying to extend the result for all $f\in W^{1,1}({\mathbb{R}^n})$.
Entropic Profiles, Maximal Motifs and the Discovery of Significant Repetitions in Genomic Sequences
2014
The degree of predictability of a sequence can be measured by its entropy and it is closely related to its repetitiveness and compressibility. Entropic profiles are useful tools to study the under- and over-representation of subsequences, providing also information about the scale of each conserved DNA region. On the other hand, compact classes of repetitive motifs, such as maximal motifs, have been proved to be useful for the identification of significant repetitions and for the compression of biological sequences. In this paper we show that there is a relationship between entropic profiles and maximal motifs, and in particular we prove that the former are a subset of the latter. As a furt…
Norms of harmonic projection operators on compact Lie groups
1988
In order to simplify the notation, we will assume throughout that G is connected, simply connected and semisimple. Sharp estimates for vp(z 0 when G = SU(2) have been obtained by Sogge [6], who proved that Vp(Zt) ~ d~ tl/v), where y(t) is the function which is affine on [1/2, 3/4] and on [3/4, 1] and is such that 7(1/2)=0, 7(3/4)=1/4, 7(1)=1. Two results in the literature give crucial estimates from below for vp(n) in the general case. The first estimate concernes the LP'-norm of the character X, : if ,~, is the highest weight of n and 0 is half the sum of the positive roots, then II x=llp,--> + 011-dimG/p" (1.2)
Sufficient conditions for supersolubility of finite groups
1998
Abstract In this paper sufficient conditions for the supersolubility of finite groups are given under the assumption that the maximal subgroups of Sylow subgroups of the group and the maximal subgroups of Sylow subgroups of the Fitting subgroup are well-situated in the group. That will improve earlier results of Srinivasan [7], Asaad et al. [1] and Ballester-Bolinches [2].
Isometric endurance test of the cervical flexor muscles - Reliability and normative reference values.
2017
Abstract Objective To obtain reference values for the isometric endurance test (IET) of the cervical flexor muscles, investigate its reproducibility, and compare the results with the maximal isometric strength test (MIST) of the cervical flexor muscles. Design Cross-sectional non-comparative study with single group repeated measurements. Methods Altogether 219 healthy females aged 20–59 years volunteered to participate in the study. The IET was performed in the supine position and MIST seated. The reproducibility was evaluated by the intraclass correlation coefficient (ICC) and an analysis described by Bland and Altman. The relationship between the two measuring methods was evaluated by Pea…
Maximal ℓ p ‐regularity of multiterm fractional equations with delay
2020
[EN] We provide a characterization for the existence and uniqueness of solutions in the space of vector-valued sequences l(p) (Z, X)for the multiterm fractional delayed model in the form Delta(alpha)u(n) + lambda Delta(beta)u(n) = Lambda u(n) + u(n-tau) + f(n), n is an element of Z, alpha, beta is an element of R+, tau is an element of Z, lambda is an element of R, where X is a Banach space, A is a closed linear operator with domain D(A) defined on X, f is an element of l(p)(Z,X) and Delta(Gamma) denotes the Grunwald-Letkinov fractional derivative of order Gamma > 0. We also give some conditions to ensure the existence of solutions when adding nonlinearities. Finally, we illustrate our resu…
An abstract doubly nonlinear equation with a measure as initial value
2007
Abstract The solvability of the abstract implicit nonlinear nonautonomous differential equation ( A ( t ) u ( t ) ) ′ + B ( t ) u ( t ) + C ( t ) u ( t ) ∋ f ( t ) will be investigated in the case of a measure as an initial value. It will be shown that this problem has a solution if the inner product of A ( t ) x and B ( t ) x + C ( t ) x is bounded below.