Search results for "Combinatorics"

Character degrees, derived length and Sylow normalizers

1997

Let P be a Sylow p-subgroup of a monomial group G. We prove that dl $ ({\Bbb N}_G (P)/P') $ is bounded by the number of irreducible character degrees of G which are not divisible by p.

Inequalities for character degrees of solvable groups

1986

A note on character degrees of solvable groups

1987

Prime Factors of Character Degrees of Solvable Groups

1987

A Characterization of Bispecial Sturmian Words

2012

A finite Sturmian word w over the alphabet {a,b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a main result that bispecial Sturmian words are exactly the maximal internal factors of Christoffel words, that are words coding the digital approximations of segments in the Euclidean plane. This result is an extension of the known relation between central words and primitive Christoffel words. Our characterization allows us to give an enumerative formula for bispecial Sturmian words. We also investigate the minimal forbidden words for the set of Sturmian wo…

Fittingmengen und lockettabschnitte

1990

Abstract The theory of Lockett sections is transferred from Fitting classes to Fitting sets. This in general works only partially; in some special groups (which I call “mobility” groups), however, among these the stable linear groups, a literal translation of the Fitting class theory is possible. As the groups relevant in outer Fitting pairs actually are mobility groups, a new way of deriving information on the Lockett section of a Fitting class arises. This is used to present a simplified, if nonsoluble, counter-example to Lockett's conjecture and to decide a related question. Also, an approach to generating Fitting classes is given.

Coriobacteriia class. nov.

2015

Construction of 3D Triangles on Dupin Cyclides

2011

This paper considers the conversion of the parametric Bézier surfaces, classically used in CAD-CAM, into patched of a class of non-spherical degree 4 algebraic surfaces called Dupin cyclides, and the definition of 3D triangle with circular edges on Dupin cyclides. Dupin cyclides was discovered by the French mathematician Pierre-Charles Dupin at the beginning of the 19th century. A Dupin cyclide has one parametric equation, two implicit equations, and a set of circular lines of curvature. The authors use the properties of these surfaces to prove that three families of circles (meridian arcs, parallel arcs, and Villarceau circles) can be computed on every Dupin cyclide. A geometric algorithm …

On generalized covering subgroups and a characterisation of ?pronormal?

1983

Introduction. The context of this note is the theory of Schunck classes and formations of finite soluble groups. In a 1972 manuscript Fischer [4] generalized the concept of an ~-covering subgroup of a group G to a (P, ~)-covering subgroup, where P is some pronormal subgroup of G, and proved universal existence (for P satisfying a stronger embedding property) in case the class ~ is a saturated formation. The fact tha t the Schunck classes are the classes ~ with the property that every group has an ~-projector [9, 4.3, 4.4; 6] (which coincides with an ~-covering subgroup in the soluble universe | [6, II.15]) raises the question whether it is possible to determine the whole range of universal …

Extremal Frobenius numbers in a class of sets

1998

For given $ A_k=\{ a_1,\ldots ,a_k \}, a_1 \le \ldots \le a_k $ coprime the Frobenius number $ {g}(A_k) $ is defined as the greatest integer ${g}$ with no representation¶¶ ${g}=\sum \limits ^k_{i=1}\,x_i\,a_i,\;x_i\in {\Bbb N}_0 $ . ¶¶A class $ {\bf A}^*_k $ is given, such that ¶¶ $ {\overline {g}}^*(k,y):= \max \{ {g}(A_k)|A_k\in {\bf A}^*_k,\, a_k\le y \} $ ¶¶has the same asymptotic behaviour as the general function¶¶ $ {\overline {g}}(k,y):= \max \{ {g}(A_k)| a_k\le y \}\, {\rm for} \, y\to \infty $ .¶¶ Furthermore, ¶¶ $ {\underline {g}}^*(k,x):= \min \{ {g}(A_k)|A_k\in {\bf A}^*_k,\, a_1\ge x \} $ ¶¶is shown to have the same order of magnitude as the general function¶¶ $ {\underline {g}…