Pal Hegedus

Central European University, Department of Mathematics and its Applications, Faculty Member

Followers

Following

Co-authors

Public Views

Interests

Uploads

Papers by Pal Hegedus

The Nottingham Group for p=2

Journal of Algebra, 2001

Download

Regular Subgroups of the Affine Group

Journal of Algebra, 2000

Download

On the number of generators needed for free profinite products of finite groups

Israel Journal of Mathematics, 2007

We provide lower estimates on the minimal number of generators of the profinite completion of fre... more We provide lower estimates on the minimal number of generators of the profinite completion of free products of finite groups. In particular, we show that if C 1 ,. .. , C n are finite cyclic groups then there exists a finite group G which is generated by isomorphic copies of C 1 ,. .. , C n and the minimal number of generators of G is n.

Download

Structure of solvable rational groups

Proceedings of the London Mathematical Society, 2005

The restrictions on K are only seemingly very strong; there are many groups satisfying them. One ... more The restrictions on K are only seemingly very strong; there are many groups satisfying them. One hopes that there is a way of simplifying these restrictions. There is a generalisation of this result to any solvable rational group; see Theorem 4.5. However, it is worth noting that in all known examples jG=O 5 0 ðGÞj is not divisible by 3, and hence Theorem 1.2 applies. Note also that from Theorem 1.1 it follows that the Sylow 2-subgroup of a rational f2; 5g-group is rational too. This curious fact is conjectured for all rational groups in the literature, with hardly any results in this direction. With some modications to the proof of Proposition 3.1, a similar result can be achieved for nite groups in which every element is conjugate to its cube. Relevant material can be found in [5]. The philosophy of the proof is the following. One uses induction on the order of the group (x 5). With a little eort it is possible to reduce (x 5.1) to the situation where the Fitting subgroup F ðGÞ is a Sylow 5-subgroup, P , and N ¼ ZðP Þ ¼ ÈðP Þ ¼ P 0 is a minimal normal subgroup of G. The aim is to show that N ¼ ½P =N; P =N ¼ 1 (x 5.2). To this end one needs detailed information about the action of G=P on P =N (x 4). In fact, G embeds into the direct sum of wreath products with fairly small, known base groups (x 4.9). Hence P =N can be written as a direct sum of corresponding subspaces X 1 =N È. .. È X n =N. Then distinct (but similar) arguments show that ½X i ; X i ¼ 1 for any i (Proposition 5.3) and ½X i ; X j ¼ 1 for any i 6 ¼ j (Proposition 5.4). The bulk of the proof consists of exhibiting and analysing the possible primitive groups and actions, always bearing in mind what is needed for the proof of the inductive step (Theorem 4.5). The more detailed Theorem 1.2 is proven in x 3. Acknowledgements. This work was incorporated into my PhD dissertation [6]. My supervisor, Jan Saxl, contributed to its development in many ways. I would like to express my gratitude to him here. 2. Preliminary results DEFINITION 2.1. Let G act on an F-space V. The action has the eigenvector property if for any v 2 V and 2 F Ã there exists g 2 G such that vg ¼ v. The next observation of Gow lies right at the heart of the argument. PROPOSITION 2.2 [4, Lemma 4]. If G acts irreducibly on an F-space V such that every g 2 G is real in G (that is, conjugate to its inverse) then G preserves a non-singular bilinear form on V. Furthermore, if the action has the eigenvector property then jF j ¼ 2; 3; 4; 8 or the form is symplectic. The following proposition is distilled from [4, Proof of Lemma 6] or alternatively from [5, A All t a as 22 and 24]. PROPOSITION 2.3. Let G be a nite rational f2; 5g-group, P 2 Syl 5 ðGÞ, and S 2 Syl 2 ðGÞ. Suppose P is normal and elementary Abelian, so write P additively. Then S acts on P linearly. Let T be any maximal subgroup in the set fC S ðvÞ j 0 6 ¼ v 2 P g and put W ¼ C P ðT Þ and N ¼ N S ðW Þ.

Download

On the Schnirelmann density of sumsets

Publications Mathématiques de l'IHÉS, 1998

A classical result of Schnirelmann asserts that σ(A + B) ≥ σ(A) + σ(B)−σ(A)σ(B) for arbitrary set... more A classical result of Schnirelmann asserts that σ(A + B) ≥ σ(A) + σ(B)−σ(A)σ(B) for arbitrary sets of integers, provided at least one of them contains 0. We establish the best possible bound that can be asserted in this case, in particular we describe all cases of equality in Schinrelmann’s theorem.

Download

When every irreducible character is a constituent of a primitive permutation character

Publicationes Mathematicae Debrecen

Noether's bound for polynomial invariants of finite groups

Arch Math, 2000

... i,n, j zδi,n, j i,n, j , 162 M. DOMOKOS and P. HEGEDU " S ARCH. MATH. ... Now we introdu... more ... i,n, j zδi,n, j i,n, j , 162 M. DOMOKOS and P. HEGEDU " S ARCH. MATH. ... Now we introduce a partial ordering on MV . First for any monomial v PMV and i P f1, ... , kg we define the ith degree counting series of v as μi d v jfj j γi j v dgj d 0, 1, 2, ... . Let v, vH be two monomials. ...

The discrete logarithmic Minkowski problem

Finite modular congruence lattices

Algebra universalis, 2005

We consider the variety of modular lattices generated by all finite lattices obtained by gluing t... more

Noether's bound for polynomial invariants of finite groups

Archiv Der Mathematik, 2000

Let G be a finite group acting linearly on the polynomial algebra CâVä .W e prove that if G is th... more Let G be a finite group acting linearly on the polynomial algebra CâVä .W e prove that if G is the semi-direct product of cyclic groups of odd prime order, then the algebra of polynomial invariants is generated by its elements whose degree is bounded by 5 jGj. As a consequence we derive that CâVä G is generated by elements

The cone volume measure of antipodal points

The number of maximal subgroups of a solvable group

Publicationes Mathematicae Debrecen, 2011

Determination of conjugacy class sizes from products of characters

Archiv Der Mathematik, 2013

In , Robinson showed that the character degrees are determined by knowing, for all n, the number ... more In , Robinson showed that the character degrees are determined by knowing, for all n, the number of ways that the identity can be expressed as a product of n commutators. Earlier, in [Str91], Strunkov showed that the existence of characters of p-defect 0 can be determined by counting solutions to certain equations involving commutators and conjugates.

Download

Noether's bound for polynomial invariants of finite groups

by Pal Hegedus and Mátyás Domokos

Archiv Der Mathematik, 2000

Let G be a finite group acting linearly on the polynomial algebra \(\Bbb C [V]\) . We prove that ... more Let G be a finite group acting linearly on the polynomial algebra \(\Bbb C [V]\) . We prove that if G is the semi-direct product of cyclic groups of odd prime order, then the algebra of polynomial invariants is generated by its elements whose degree is bounded by \({5 \over 8}|G|\) . As a consequence we derive that \(\Bbb C [V]^G\) is generated by elements of degree \(\leqq {3 \over 4}|G|\) for any non-cyclic group G. This sharpens the improved bound for Noether's Theorem due to Schmid.

The Nottingham Group for p = 2

Journal of Algebra, 2001

In this paper I consider the Nottingham group over a finite field of characteristic 2. I obtain a... more In this paper I consider the Nottingham group over a finite field of characteristic 2. I obtain a number of results previously known only for Nottingham groups in odd characteristic. For example, I obtain information on the derived series and I prove that the Nottingham group is hereditarily just-infinite as a pro-2 group. As a consequence, the Nottingham group over

Structure of solvable rational groups

Proceedings of The London Mathematical Society, 2005

Regular Subgroups of the Affine Group

Journal of Algebra, 2000

Download

Finite modular congruence lattices

by Pal Hegedus and Péter Pálfy

Algebra Universalis, 2005

We consider the variety of modular lattices generated by all finite lattices obtained by gluing t... more

On the number of generators needed for free profinite products of finite groups

We provide lower estimates on the minimal number of generators of the profinite completion of fre... more We provide lower estimates on the minimal number of generators of the profinite completion of free products of finite groups. In particular, we show that if C_1,...,C_n are finite cyclic groups then there exists a finite group G which is generated by isomorphic copies of C_1,...,C_n and the minimal number of generators of G is n.

Download

Pal Hegedus

Uploads

Papers by Pal Hegedus

Log In