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Maximal clones and maximal permutation groups

Péter P. Pálfy — 2007

Discussiones Mathematicae - General Algebra and Applications

A fundamental result in universal algebra is the theorem of Rosenberg describing the maximal subclones in the clone of all operations over a finite set. In group theory, the maximal subgroups of the symmetric groups are classified by the O'Nan-Scott Theorem. We shall explore the similarities and differences between these two analogous major results. In addition, we show that a primitive permutation group of diagonal type can be maximal in the symmetric group only if its socle is the direct product...

Expansion in S L d ( 𝒪 K / I ) , I square-free

Péter P. Varjú — 2012

Journal of the European Mathematical Society

Let S be a fixed symmetric finite subset of S L d ( 𝒪 K ) that generates a Zariski dense subgroup of S L d ( 𝒪 K ) when we consider it as an algebraic group over m a t h b b Q by restriction of scalars. We prove that the Cayley graphs of S L d ( 𝒪 K / I ) with respect to the projections of S is an expander family if I ranges over square-free ideals of 𝒪 K if d = 2 and K is an arbitrary numberfield, or if d = 3 and K = ℚ .

Including eigenvalues of the plane Orr-Sommerfeld problem

Peter P. Klein — 1993

Applications of Mathematics

In an earlier paper [5] a method for eigenvalue inclussion using a Gerschgorin type theory originating from Donnelly [2] was applied to the plane Orr-Sommerfeld problem in the case of a pure Poiseuile flow. In this paper the same method will be used to deal Poiseuile and Couette flow. Potter [6] has treated this case before with an approximative method.

A contribution to infinite disjoint covering systems

János Barát;  Péter P. Varjú — 2005

Journal de Théorie des Nombres de Bordeaux

Let the collection of arithmetic sequences { d i n + b i : n ∈ ℤ } i ∈ I be a disjoint covering system of the integers. We prove that if d i = p k q l for some primes p , q and integers k , l ≥ 0 , then there is a j ≠ i such that d i | d j . We conjecture that the divisibility result holds for all moduli. A disjoint covering system is called saturated if the sum of the reciprocals of the moduli is equal to 1 . The above conjecture holds for saturated systems with d i such that the product of its prime factors is at most 1254 .

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