Search results for "Combinatorics"

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.

Soluble groups with their centralizer factor groups of bounded rank

2007

Abstract For a group class X , a group G is said to be a C X -group if the factor group G / C G ( g G ) ∈ X for all g ∈ G , where C G ( g G ) is the centralizer in G of the normal closure of g in G . For the class F f of groups of finite order less than or equal to f , a classical result of B.H. Neumann [Groups with finite classes of conjugate elements, Proc. London Math. Soc. 1 (1951) 178–187] states that if G ∈ C F f , the commutator group G ′ belongs to F f ′ for some f ′ depending only on f . We prove that a similar result holds for the class S r ( d ) , the class of soluble groups of derived length at most d which have Prufer rank at most r . Namely, if G ∈ C S r ( d ) , then G ′ ∈ S d…

Brauer's fixed-point-formula as a consequence of Thompson's order-formula

1991

Triangular Bézier Surfaces of Minimal Area

2003

We study some methods of obtaining approximations to surfaces of minimal area with prescribed border using triangular Bezier patches. Some methods deduced from a variational principle are proposed and compared with some masks.

Rank formulae for factorized groups

1991

The following inequalities for the torsion-free rank r0(G) of the group G=AB and for the p∞-rank rp(G) of the soluble-by-finite group G=AB are stated: $$\begin{gathered} r_0 (G) \leqslant r_0 (A) + r_0 (B) - r_0 (A \cap B), \hfill \\ r_p (G) \leqslant r_p (A) + r_p (B) - r_p (A \cap B). \hfill \\ \end{gathered} $$

Braiding minimal sets of vector fields

2002

We extend a classical but fundamental theorem of knot and braid theories to describe the geometry of nonsingular minimal sets of 3-dimensional flows.

The Influence of H. Grassmann on Italian Projective N-Dimensional Geometry

1996

On May 29, 1883, Corrado Segre took his doctorate in Turin (Torino), under Enrico D’Ovidio’s guidance. His thesis (Segre 1884a,b) was published one year later in the Journal of the local Academy of Science, and after a short time it became a fundamental starting point for the development of Italian projective n-dimensional geometry.

Doubly nonlinear equations with unbounded operators

2004

Abstract The solvability of the evolution system v′(t)+ B (t)u(t)∋ f (t),v(t)∈ A (t)u(t) , 0 A (t) are bounded, possibly degenerate, subdifferentials and B (t) are unbounded subdifferentials.

A variation on theorems of Jordan and Gluck

2006

Abstract Gluck proved that any finite group G has an abelian subgroup A such that | G : A | is bounded by a polynomial function of the largest degree of the complex irreducible characters of G . This improved on a previous bound of Isaacs and Passman. In this paper, we present a variation of this result that looks at the number of prime factors. All these results, in turn, may be seen as variations on the classical theorem of Jordan on linear groups.

Zu einem Satz von Isaacs �ber das Casus-Irreducibilis Ph�nomen

2000

Let \(\Omega \) be a field (of characteristic 0). A prime p is called “bose” (naughty) if \(\Omega \) contains all p-th roots of unity. In this paper the theorem is proved: Let K be an admissible subfield of \(\Omega \) (i.e. for each prime p K contains all p-th roots of unity lying in \(\Omega \)), a an algebraic element of \(\Omega /K\) which is contained in a repeated radical extension of K lying in \(\Omega \). Furthermore let the normal hull L of a over K be contained in \(\Omega \). Then all prime divisors of \(\mid L : K \mid \) are naughty (and L is a repeated radical extension of K with naughty prime exponents). This result generalises a theorem of Isaacs [1] who treats the case \(…