a finite group $g$ satisfies the on-prime power hypothesis for conjugacy class sizes if any two conjugacy class sizes $m$ and $n$ are either equal or have a common divisor a prime power. taeri conjectured that an insoluble group satisfying this condition is isomorphic to $s times a$ where $a$ is abelian and $s cong psl_2(q)$ for $q in {4,8}$. we confirm this conjecture.

These notes are based on Saltman’s seminal work on the Brauer group Br(K) of the function field K of a p-adic curve XQp . In [S1] and [S2], Saltman showed the index of an element in the prime-to-p part of Br(K) divides the square of its period, and that all division algebras of prime degree q 6= p are cyclic. He also gave a geometric criterion for a class of prime period q 6= p to have index q....

We propose a technique for obtaining solutions to ordinary differential equations. A system of differential equations sometimes has multiple solutions with distinct features. Prime ideal decomposition can be used for extracting the desired solution from these solutions. Solutions to algebraic equations contain many parameters, and in such a case, prime ideal decomposition is less tractable. As ...

It is shown that an even partition A∪B of the set R = {1, 2, . . . , p− 1} of positive residues modulo an odd prime p is the partition into quadratic residues and quadratic non-residues if and only if the elements of A and B satisfy certain additive properties, thus providing a purely additive characterization of the set of quadratic residues. 1 Additive properties of quadratic residues An inte...

The initial motivation of the present paper is the following problem of Erd6s and Woods, whose solution would be of interest in logic (see [3, 6, 11, 10, 16]): Does there exist an integer k >=2 with the following property : i f x and y are positive integers such that for l<=i<=k, the two numbers x+ i and y+i have the same prime factors, then x=y. For each integer n->2, let us denote by Supp (n)...

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

In this paper we introduce the optimal solution for a simple and yet practical inventory policy with the important characteristic which eliminates the uncertainty in demand for suppliers. In this new policy which is different from the classical inventory policies, the time interval between any two consecutive orders is fixed and the quantity of each order is one. Assuming the fixed ordering cos...

OBJECTIVE To evaluate the effect of an in vitro challenge (NaOCl immersion) on microtensile bond strength (MTBS) of five adhesive systems to dentin. METHODS Flat dentin surfaces from 40 molars were bonded with three total-etch adhesives (Single Bond, Prime&Bond NT and the experimental Prime&Bond XP), and two self-etching agents (Clearfil SE Bond and Etch&Prime 3.0). Composite build-ups were c...