Search results for "character"

Sylow subgroups, exponents, and character values

2019

If G G is a finite group, p p is a prime, and P P is a Sylow p p -subgroup of G G , we study how the exponent of the abelian group P / P ′ P/P’ is affected and how it affects the values of the complex characters of G G . This is related to Brauer’s Problem 12 12 . Exactly how this is done is one of the last unsolved consequences of the McKay–Galois conjecture.

On Large Orbits of Actions of Finite Soluble Groups: Applications

2020

The main aim of this survey paper is to present two orbit theorems and to show how to apply them to obtain a result that can be regarded as a significant step towards the solution of Gluck’s conjecture on large character degrees of finite soluble groups. We also show how to apply them to solve questions about intersections of some conjugacy families of subgroups of finite soluble groups.

Degree-problems I squarefree character degrees

1985

A remark on the character-degrees of somep-groups

1992

Chern classes of the moduli stack of curves

2005

Here we calculate the Chern classes of ${\bar {\mathcal M}}_{g,n}$, the moduli stack of stable n-pointed curves. In particular, we prove that such classes lie in the tautological ring.

Boundary Regularity for the Porous Medium Equation

2018

We study the boundary regularity of solutions to the porous medium equation $u_t = \Delta u^m$ in the degenerate range $m>1$. In particular, we show that in cylinders the Dirichlet problem with positive continuous boundary data on the parabolic boundary has a solution which attains the boundary values, provided that the spatial domain satisfies the elliptic Wiener criterion. This condition is known to be optimal, and it is a consequence of our main theorem which establishes a barrier characterization of regular boundary points for general -- not necessarily cylindrical -- domains in ${\bf R}^{n+1}$. One of our fundamental tools is a new strict comparison principle between sub- and superpara…

Huppert's conjecture for character codegrees

2021

Characteristic numbers of non‐autonomous emden‐fowler type equations

2006

We consider the Emden‐Fowler equation x” = ‐q(t)|x|2εx, ε > 0, in the interval [a,b]. The coefficient q(t) is a positive valued continuous function. The Nehari characteristic number An associated with the Emden‐Fowler equation coincides with a minimal value of the functional [] over all solutions of the boundary value problem x” = ‐q(t)|x|2εx, x(a) = x(b) = 0, x(t) has exactly (n ‐ 1) zeros in (a, b). The respective solution is called the Nehari solution. We construct an example which shows that the Nehari extremal problem may have more than one solution. First Published Online: 14 Oct 2010

Total curvatures of compact complex submanifolds in $$C/P^n$$

1995

LetM be a complex submanifold in\(C/P^n\). We define the total curvatures ofM and we get a local interpretation of them. Finally, we give a topological characterization for the total (non-absolute) curvature of complex hypersurfaces in\(C/P^n\).

Bifurcations of links of periodic orbits in non-singular Morse–Smale systems with a rotational symmetry on S3

2000

Abstract In this paper we consider a rotational symmetry on a non-singular Morse–Smale (NMS) system analyzing the restrictions this symmetry imposes on the links defined by the set of its periodic orbits and to the appearance of local generic codimension one bifurcations in the set of NMS flows on S 3 . The topological characterization is obtained by writing the involved links in terms of Wada operations. It is also obtained that symmetry implies that in general bifurcations have to be multiple. On the other hand, we also see that there exists a set of links that cannot be related to any other by sequences of this kind of bifurcation.