Groups with regular automorphisms of order four

Mathematische Zeitschrift -     

Groups with a centralizer of sixth order

Let G be a finite fusion-simple group with a self-centralizing subgroup A of sixth order. It is proved that if the centralizer of the involution from A is an unsolvable subgroup of G of an odd index, then G is isomorphic with the Janko group J₁.Translated from Matematicheskie Zametki, Vol. 22, No. 1, pp. 153–159, July, 1977.The author thanks A. I. Starostin for the formulation of the problem and guidance.     

Groups with the same order and degree pattern

The degree pattern of a finite group has been introduced in [18].A group M is called k-fold OD- characterizable if there exist exactly k non-isomorphic finite groups having the same order and degree pattern as M .In particular,a 1-fold OD-characterizable group is simply called OD-characterizable.It is shown that the alternating groups A m and A m+1 ,for m = 27,35,51,57,65,77,87,93 and 95,are OD-characterizable,while their automorphism groups are 3-fold OD-characterizable.It is also shown that the symmetric groups S m+2 ,for m = 7,13,19,23,31,37,43,47,53,61,67,73,79,83,89 and 97,are 3-fold OD-characterizable.From this,the following theorem is derived.Let m be a natural number such that m 100.Then one of the following holds: (a) if m = 10,then the alternating groups A m are OD-characterizable,while the symmetric groups S m are OD- characterizable or 3-fold OD-characterizable;(b) the alternating group A 10 is 2-fold OD-characterizable;(c) the symmetric group S 10 is 8-fold OD-characterizable.This theorem completes the study of OD-characterizability of the alternating and symmetric groups A m and S m of degree m 100.     

Groups with three real valued irreducible characters

We obtain strong restrictions on the structure of a Sylow 2-subgroup of a group with at most three real valued irreducible characters. This extends results of Iwasaki, who studied groups with at most two real valued irreducible characters. This research was partially supported by the Spanish Ministerio de Educación y Ciencia, MTM2004-06067-C02-01 and MTM2004-04665, and the FEDER. The first author was also supported by the Programa Ramón y Cajal and the Generalitat Valenciana.     

Non-periodic Riemann examples with handles

We show the existence of 1-parameter families of non-periodic, complete, embedded minimal surfaces in Euclidean space with infinitely many parallel planar ends. In particular we are able to produce finite genus examples and quasi-periodic examples of infinite genus.     

Combinatorial handles and manifolds with boundary

In this work we complete the study ofcombinatorial handles in (n+1)-coloured graphs with boundary, introduced in [G₁], [L] and [GV] for graphs with empty boundary and in [BGV] for 3-coloured graphs with boundary. In particular, we study the cancelling of a combinatorial handle from an (n+1)-coloured graph and its effects on the associated complex.Work performed under the auspices of the G.N.S.A.G.A. — C.N.R., and within the Project Geometria reale e complessa, supported by M.U.R.S.T. of Italy.     

Isoperimetric constants of manifolds with small handles

Mathematische Zeitschrift -     

Surfaces of order three with a peak! I

A surfaceF of order three in the real projective three space is met by every line, not inF, in at most three points. We present a synthetic theory of these surfaces based upon a concept of differentiability. A pointv inF is a peak ifF has a unique tangent atvs and it does not lie inF. We classify theF with a peak by determining the number of lines inF and their configuration. We describe each surface by determining the tangent plane sections ofF at the differentiable points.     

Embeddedsdirk-methods of basic order three

The purpose of this report is to construct 3-stage SDIRK-methods (Singly Diagonally Implicit Runge-Kutta) to be used for the code SIMPLE. The local error control is performed by embedding techniques. Pairs with and without extrapolation are given.Dedicated to Germund Dahlquist, on the occasion of his 60'th birthday.This work was supported by NATO, grant 96.80/D1.     

Surfaces of order three with a peak. II

In [1], we presented a theory of surfaces of order three in real projective three-spaceP ³. In the present paper, we prove that a surfaceF of order three with a peak contains one, two or three lines and there are four types of suchF based upon the configuration of these lines. We describe eachF by determining the existence and the distribution of elliptic, parabolic and hyperbolic points; that is, points ofF not lying on any line contained inF.     

Groups with elementary abelian commutant of at most p 2th order

We obtain a representation of nilpotent groups with a commutant of the type (p) or (p, p) that has the form of a product of two normal subgroups. One of these subgroups is constructively described as a Chernikov p-group of rank 1 or 2, and the other subgroup has a certain standard form. We also obtain a representation of nonnilpotent groups with a commutant of the type (p) or (p, p) in the form of a semidirect product of a normal subgroup of the type (p) or (p, p) and a nilpotent subgroup with a commutant of order p or 1. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 4, pp. 534–539, April, 1998.     

Groups of order 24 and their endomorphism semigroups

It is proved that among the finite groups of order 24 only the binary tetrahedral group is not determined by its endomorphism semigroup in the class of all groups. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 3, pp. 155–172, 2005.