Let G be a finite group and let δ(G) be the number of prime order subgroups of G. We determine the groups G with the property δ(G) > |G|/2− 1, extending earlier work of C. T. C. Wall, and we use our classification to obtain new results on the generation of near-rings by units of prime order. 2000 Mathematics subject classification: primary 20D06; secondary 20D10, 16Y30.

Abstract Based on maximally entangled states, we explore the constructions of mutually unbiased bases in bipartite quantum systems. We present a new way to construct by difference matrices theory combinatorial designs. In particular, establish q with − 1 and one product basis <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="i...

Superconductivity in strongly correlated electrons can emerge out from a normal state that is beyond the Landau's Fermi liquid paradigm, often dubbed as "non-Fermi liquid". While theory for non-Fermi still not yet conclusive, recent study on exactly-solvable Hatsugai-Kohmoto (HK) model has suggested ground whose Green's function resembles Yang-Rice-Zhang ansatz cuprates [P. W. Phillips, L. Yeo ...

‎Let $G$ be a group with identity $e.$ Let $R$ be a $G$-graded‎ ‎commutative ring and $M$ a graded $R$-module‎. ‎In this paper‎, ‎we‎ ‎introduce several results concerning graded classical prime‎ ‎submodules‎. ‎For example‎, ‎we give a characterization of graded‎ ‎classical prime submodules‎. ‎Also‎, ‎the relations between graded‎ ‎classical prime and graded prime submodules of $M$ are studied‎.‎

Suppose P is a set of primes, such that for every p ∈ P , every prime factor of p − 1 is also in P . We apply a new sieve method to show that either P contains all of the primes or the counting function of P is O(x) for some c > 0, where c depends only on the smallest prime not in P . Our proof makes use of results connected with Artin’s primitive root conjecture.

2 Powering Stage (Sketch) 2.1 Parameter Effects In this section, we will be sketchy about some details. Entering the powering stage, we have an input constraint graph denoted (G, C). G is an a (n, d, λ)-expander, with λ < d universal constants, and the constraints are over some fixed constant alphabet Σ = Σ0. Our goal is to produce a new constraint graph (G′, C ′) with a larger gap. We will den...

We present an algorithm for generating elliptic curves of prime order over Optimal Extension Fields suitable for use in cryptography. The algorithm is based on the theory of Complex Multiplication. Furthermore, we demonstrate the efficiency of the algorithm in practice by giving practical running times. In addition, we present statistics on the number of cryptographically strong elliptic curves...

We give numerical and theoretical evidence in support of the conjecture of Dressler that between any two positive integers having the same prime factors there is a prime. In particular, it is shown that the abc conjecture implies that the gap between two consecutive such numbers a < c is a1/2− , and it is shown that this lower bound is best possible. Dressler’s conjecture is verified for values...

We consider the form factors for radiative semileptonic decays $\bar{B}(v) \rightarrow D^{(*)}(v') \ell {\bar \nu}_\ell \gamma$ in kinematic region where photon momentum, $k$, is small enough that heavy quark symmetry (HQS) can be applied without radiated changing velocity (i.e., $v^{(\prime)} \cdot k < m_{(b,c)}$). find HQS remarkably powerful, leaving only four new undetermined at leading ord...