Normal analytic polyhedra in ℂ2 with a noncompact automorphism group

Let P be a bounded analytic polyhedron in ℂ² whose boundary is smooth except for normal crossing singularities. We show that P is a holomorphic quotient of the bidisc, if its automorphism group is noncompact.     

On a certain ideal of Külshammer in the centre of a group algebra

Let G be a finite group and let F be a splitting field of characteristic $ p > 0 $ p > 0 . We show that I² = E₀, where I is a certain ideal of the centre Z of FG, and E₀ is the span of the block idempotents of defect zero.     

On the simplicity of the automorphism group ofP(ω)/fin

Summary We prove that the automorphism group ofP()/fin remains simple if ₂ Cohen reals are added to a model of ZFC+CH.This paper is based on a part of author's Dissertation [4] written under the supervision of Professor Sabine Koppelberg whom the author would like to thank for her encouragement during the preparation of the thesis. Thanks are also due to the referee for some valuable suggestions on improvement of the formulation     

Characterization of convex domains in ℂ<Superscript>2</Superscript> with non-compact automorphism group

In the field of several complex variables, the Greene-Krantz Conjecture, whose consequences would be far reaching, has yet to be proven. The conjecture is as follows: Let D be a smoothly bounded domain in ?ⁿ. Suppose there exists {g _j} ? Aut(D) such that {g _j(z)} accumulates at a boundary point p ∈ ?D for some z ∈ D. Then ?D is of finite type at p. In this paper, we prove the following result, yielding further evidence to the probable veracity of this important conjecture: Let D be a bounded convex domain in ?² with C ² boundary. Suppose that there is a sequence {g _j} ? Aut(D) such that {g _j(z)} accumulates at a boundary point for some point z ∈ D. Then if p ∈ ?D is such an orbit accumulation point, ?D contains no non-trivial analytic variety passing through p.     

On the automorphism groups of β-derived planes

This paper contains some general results about the automorphism group H of PG(3,q) leaving a -derived spread F invariant. The main result asserts that H contains a cyclic subgroups M^*, whose order divides (q+1)/2. In particular, H is not trivial. In terms of translation planes this means that the translation complement of any -derived plane always admits some collineations which are not dilatations.Research partially supported by M.P.I. (Research project Strutture Geometriche Combinatorie e loro Applicazioni).     

On the sphericity of the subgroup PSL2(ℝ) in the group of diffeomorphisms of the circle

It is shown that the group PSL₂(?) is a spherical subgroup in the group of C³-diffeomorphisms of the circle.     

On the T∘-slices of a finite group

A slice $(G,S)$ of finite groups is a pair consisting of a finite group G and a subgroup S of G. In this paper, we show that some properties of finite groups extend to slices of finite groups. In particular, by analogy with B-groups, we introduce the notion of $T^{°}$-slice, and show that any slice of finite groups admits a largest quotient $T^{°}$-slice.     

On the torsion in K_2 of a field

For a field F,let Gn(F) = {{a,Φn(a)} ∈ K2(F) | a,Φn(a) ∈ F*},where Φn(x) is the n-th cyclotomic polynomial.At first,by using Faltings' theorem on Mordell conjecture it is proved that if F is a number field and if n = 4,8,12 is a positive integer having a square factor then Gn(F) is not a subgroup of K2(F),and then by using the results of Manin,Grauert,Samuel and Li on Mordell conjecture theorem for function fields,a similar result is established for function fields over an algebraically closed field.     

On the ℂ-differentiability of mappings of Banach spaces

We study the monogeneity conditions for -differentiable mappings of domains of a Banach space and establish criteria of -differentiability of a mapping at a point.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1336–1342, October, 1994.     

On the unit group and the class number¶of certain composita of two real quadratic fields

The purpose of this paper is to exhibit a new family of real bicyclic biquadratic fields K for which we can write the Hasse unit index of the group generated by the units of the three quadratic subfields in the unit group E _K of K. As a byproduct, one can explicitly relate the class number of K with the product of the class numbers of the three quadratic subfields. Received: 25 July 2000 / Revised version: 12 December 2000     

What is the probability an automorphism fixes a group element?

Extending the notion of probability to the automorphisms of a group, we find the probability of an arbitrarily chosen automorphism of a group fixing an arbitrary element of the group.     

On the\bar \partial equation in weightedL 2 norms in ℂ1equation in weightedL 2 norms in ℂ1

For a large class of subharmonicφ, the equation is studied in . Pointwise upper bounds are derived for the distribution kernels of the canonical solution operator and of the orthogonal projection onto the space of entire functions inH. Existence theorems inL ^p norms are derived as a corollary. A class of counterexamples, related to the failure of to be analytic-hypoelliptic on certain CR manifolds, is discussed. Communicated by Steven Krantz     

On the Chermak–Delgado lattice of a finite group

Abstract

By imposing conditions upon the index of a self-centralizing subgroup of a group, and upon the index of the center of the group, we are able to classify the Chermak-Delgado lattice of the group. This is our main result. We use this result to classify the Chermak-Delgado lattices of dicyclic groups and of metabelian p-groups of maximal class.     

On the closure of the sum of two uniform algebras on compact sets in ℂ

Necessary and sufficient conditions on a compact set X in ? and a self-homeomorphism ψ of the plane ? are studied under which any function continuous on X can be approximated uniformly on X by functions of the form p + h ° ψ, where p is a polynomial in a complex variable and h is a rational function whose poles belong to the bounded components of the complement to the compact set ψ(X).     

Connectedness of the invertibles in certain nest algebras of order type ω

We solve the connectedness problem for a class of nests of order type ω with finite dimensional atoms.     

On the normalizer of a Gaschütz system of a finite soluble group

The notion of a Gaschütz system of a finite soluble group was introduced by S. F. Kamornikov in 2008 (this is a set of complements of crowns of pairwise nonisomorphic non-Frattini factors of a chief series of the group). In the present paper, properties of Gaschütz systems are investigated. In particular, we calculate the number of Gaschütz systems in a finite soluble group and prove their conjugacy, obtain a connection between mathfrakN mathfrak{N} -prefrattini subgroups and normalizers of Gaschütz systems, and investigate factorizations of the normalizer of a Gaschütz system.     

On the CR analogue of Obata’s theorem in a pseudohermitian 3-manifold

In this paper, we first prove the CR analogue of Obata’s theorem on a closed pseudohermitian 3-manifold with zero pseudohermitian torsion. Secondly, instead of zero torsion, we have the CR analogue of Li-Yau’s eigenvalue estimate on the lower bound estimate of positive first eigenvalue of the sub-Laplacian in a closed pseudohermitian 3-manifold with nonnegative CR Paneitz operator P ₀. Finally, we have a criterion for the positivity of first eigenvalue of the sub-Laplacian on a complete noncompact pseudohermitian 3-manifold with nonnegative CR Paneitz operator. The key step is a discovery of integral CR analogue of Bochner formula which involving the CR Paneitz operator. This research was supported in part by the NSC of Taiwan.