Search results for "General Mathematics"

Transitive factorizations in the hyperoctahedral group

2008

The classical Hurwitz enumeration problem has a presentation in terms of transitive factor- izationsin the symmetric group. This presentationsuggestsageneralizationfromtypeAto otherfinite reflection groups and, in particular, to type B.W e study this generalization both from ac ombinatorial and a geometric point of view, with the prospect of providing am eans of understanding more of the structure of the moduli spaces of maps with an S2-symmetry. The type A case has been well studied and connects Hurwitz numbers to the moduli space of curves. W ec onjecture an analogous setting for the type B case that is studied here. 1I ntroduction Transitive factorizations of permutations into transposit…

The $Q_{ \alpha}$-restriction problem

2019

When is a 𝑝-block a 𝑞-block?

1997

Let p p and q q be distinct prime numbers and let G G be a finite group. If B p B_{p} is a p p -block of G G and B q B_{q} is a q q -block, we study when the set of ordinary irreducible characters in the blocks B p B_{p} and B q B_{q} coincide.

Über den Rang der projektiven Darstellung von Kettengeometrien auf Grassmann-Mannigfaltigkeiten

1985

Zur Existenz von Lösungen gewisser Randwertaufgaben

1971

With the aid of some known results about integral equations of the Hammerstein type there is proofed an existence theorem for the following class of boundary value problems−y″−l 2 y′=f(x,y),y(a)=y(b)=0,l 2>0 mit|f(x, y)|=0,l 3 (x)>0. The existence range is determined by the greatest eigenvalue of some linear problem.

Metric properties of the group of area preserving diffeomorphisms

2001

Area preserving cliffeoinorpliisms of the 2-disk which are identity near the boundary form a group D2 wllich can be equipped, usin-g tlhe L2nlorm on its Lie algebra, with a right invariant metric. Witll tllis metric the diameter of D2 is infinite. In this paper we sl-iow that D2 contains quasiisometric embeddings of any finitely generated free group and any finitely generated abelian free group.

A space on which diameter-type packing measure is not Borel regular

1999

We construct a separable metric space on which 1-dimensional diameter-type packing measure is not Borel regular.

Deuring’s mass formula of a Mumford family

2015

We study the Newton polygon jumping locus of a Mumford family in char p p . Our main result says that, under a mild assumption on p p , the jumping locus consists of only supersingular points and its cardinality is equal to ( p r − 1 ) ( g − 1 ) (p^r-1)(g-1) , where r r is the degree of the defining field of the base curve of a Mumford family in char p p and g g is the genus of the curve. The underlying technique is the p p -adic Hodge theory.

Vertices for characters of $p$-solvable groups

2002

Suppose that G is a finite p-solvable group. We associate to every irreducible complex character X ∈ Irr(G) of G a canonical pair (Q, δ), where Q is a p-subgroup of G and δ ∈ Irr(Q), uniquely determined by X up to G-conjugacy. This pair behaves as a Green vertex and partitions Irr(G) into families of characters. Using the pair (Q, δ), we give a canonical choice of a certain p-radical subgroup R of G and a character η ∈ Irr(R) associated to X which was predicted by some conjecture of G. R. Robinson.

VARIATIONS ON THOMPSON'S CHARACTER DEGREE THEOREM

2001

If P is a Sylow- p -subgroup of a finite p -solvable group G , we prove that G^\prime \cap \bf{N}_G(P) \subseteq {P} if and only if p divides the degree of every irreducible non-linear p -Brauer character of G. More generally if π is a set of primes containing p and G is π-separable, we give necessary and sufficient group theoretic conditions for the degree of every irreducible non-linear p -Brauer character to be divisible by some prime in π. This can also be applied to degrees of ordinary characters.