Search results for "Number"

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 …

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|.

Variations on a Theorem of Fine & Wilf

2001

In 1965, Fine & Wilf proved the following theorem: if (fn)n≥0 and (gn)n≥0 are periodic sequences of real numbers, of periods h and k respectively, and fn = gn for 0 ≤ n ≤ h+k-gcd(h, k), then fn = gn for all n ≥ 0. Furthermore, the constant h + k - gcd(h, k) is best possible. In this paper we consider some variations on this theorem. In particular, we study the case where fn ≤ gn instead of fn = gn. We also obtain a generalization to more than two periods.

Polyomino Number Theory (II)

2003

Polyominoes are connected plane figures formed of joining unit squares edge to edge. We have a monomino, a domino, two trominoes named I and V, five tetrominoes named I, L, N, O and T, respectively, and twelve pentominoes (a registered trademark of Solomon W. Golomb) named F, I, L, N, P, T, U, V, W, X, Y and Z respectively.

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.

Approximation Operators of Binomial Type

1999

Our objective is to present a unified theory of the approximation operators of binomial type by exploiting the main technique of the so- called “ umbral calculus” or “finite operator calculus” (see [18], [20]-[22]). Let us consider the basic sequence (bn)n≥0 associated to a certain delta operator Q. By supposing that b n (x) ≥ 0, x ∈ [0, ∞), our purpose is to put in evidence some approximation properties of the linear positive operators (L Q n ) n≥1 which are defined on C[0,1] by \( L_n^Qf = \sum\limits_{k = 0}^n {\beta _n^Q{,_k}f\left( {\frac{k}{n}} \right),\beta _{n{,_k}}^Q\left( x \right): = } \frac{1}{{{b_n}\left( n \right)}}\left( {\begin{array}{*{20}{c}} n \\ k \end{array}} \right){b_…

On ∗-polynomial identities for n × n matrices

1990

Numerical bounds for semi-stable families of curves or of certain higher-dimensional manifolds

2005

Given an open subset U U of a projective curve Y Y and a smooth family f : V → U f:V\to U of curves, with semi-stable reduction over Y Y , we show that for a subvariation V \mathbb {V} of Hodge structures of R 1 f ∗ C V R^1f_*\mathbb {C}_V with rank ( V ) > 2 \textrm {rank} (\mathbb {V})>2 the Arakelov inequality must be strict. For families of n n -folds we prove a similar result under the assumption that the ( n , 0 ) (n,0) component of the Higgs bundle of V \mathbb {V} defines a birational map.

Hyperidentities of some generalizations of lattices

1998

In the paper we present bases and hyperbases of hyperidentities of some generalizations of the variety L of all lattices and the variety D of distributive lattices. We describe the form of hyperidentities of some varieties with two binary operations.