Table Of ContentAlgebra
A.G. Kurosh 1908-1971
Algebra
Proceedings of the International Algebraic Conference
on the Occasion of the 90th Birthday of A. G. Kurosh
Moscow, Russia, May 25-30, 1998
Editor
Yuri Bahturin
W
DE
G
Walter de Gruyter · Berlin · New York 2000
Editor
Yuri Bahturin
Dept. of Mathematics and Statistics
University of Newfoundland
St. John's, NF, Canada
7997 Mathematics Subject Classification:
03-03, 03B70, 08-XX, 13-XX, 14-XX, 15-XX, 16-XX, 17-XX, 18-XX, 20-XX, 22-XX, 62-XX,
68-XX
Keywords:
Groups, rings, modules, Lie algebras, algebraic groups, representations, algebraic varieties,
universal algebras, computer algebra
© Printed on acid-free paper which falls within the guidelines of the ANSI
to ensure permanence and durability.
Library of Congress — Cataloging-in-Publication Data
International Algebraic Conference on the Occasion of the 90th
Birthday of A. G. Kurosh (1998 : Moscow, Russia)
Algebra: proceedings of the International Algebraic Confe-
rence on the Occasion of the 90th Birthday of A. G. Kurosh,
Moscow, Russia, May 25-30, 1998 / editor, Yuri Bahturin.
p. cm.
Includes bibliographical references.
ISBN 3 11 016399 3 (alk. paper)
I. Algebra - Congresses. I. Kurosh, A. G. (Aleksandr Gen-
nadievich) II. Bakhturin, IU. A.
QA150 .152 1998
512-dc21
99-058019
Die Deutsche Bibliothek — C1P-Einheitsaufnähme
Algebra : proceedings of the International Algebraic Confe-
rence on the Occasion of the 90th Birthday of A. G. Kurosh,
Moscow, Russia, May 25-30, 1998 / Ed. Yuri Bahturin. -
Berlin ; New York : de Gruyter, 2000
ISBN 3-11-016399-3
© Copyright 2000 by Walter de Gruyter GmbH & Co. KG, D-10785 Berlin
All rights reserved, including those of translation into foreign languages. No part of this book
may be reproduced or transmitted in any form or by any means, electronic or mechanical,
including photocopy, recording or any information storage and retrieval system, without permis-
sion in writing from the publisher.
Printed in Germany.
Typeset using the authors' T X files: L Zimmermann, Freiburg.
E
Printing: WB-Druck GmbH & Co., Rieden/Allgäu. Binding: Lüderitz & Bauer-GmbH, Berlin.
Cover design: Thomas Bonnie, Hamburg.
Preface
The International Algebraic Conference, dedicated to the memory of one of the
forerunners of modern algebra Alexander Gennadievich Kurosh, was held at Mos-
cow Lomonosov State University from May 25 to May 30, 1998. More than 230
participants from at least 25 countries around the world attended the event. Most
of them delivered lectures or shorter talks, about 160 in total. The Organizing
Committee (Head: Alexei Ivanovich Kostrikin) had selected 25 plenary lectures
and a number of principal sectional talks. Six Section Committees formed the
remaining portion of the program. The names of the sections give an idea of the
diversity of interests of the participants.
Section 1. Group Theory.
Section 2. Theory of Rings and Modules, Homological Algebra and fC-theory.
Section 3. Lie Groups and Lie Algebras, Invariant Theory, Algebraic Groups.
Section 4. Algebraic Geometry, Algebraic Number Theory, Commutative Algebra.
Section 5. Algebraic Systems.
Section 6. Computer Algebra and Algorithmic Problems.
The main organizing force of the conference was formed by the faculty, staff
and the graduate students of the Department (= Chair) of Higher Algebra. The
administration of Moscow State University was also of great assistance, especially
with the accommodation of the participants. Some expenses were covered by
grants of the Russian Foundation for the Basic Research (Grant 98-01-10041), IN-
TAS (Grant 98-MO48) and Pro Mathematica Fond. These grants assisted with
the travel (actually, made it possible at all!) of the mathematicians from a num-
ber of economically troubled countries and the publishing of the materials of the
Conference, including this volume. The organizers greatly appreciate the support
of Moscow University and the foundations mentioned.
The atmosphere of the Conference was very friendly and businesslike. All the
talks contained new research information and, in quite a few cases, the solutions
to known problems, or simply outstanding achievements.
Some of the talks resulted in the papers that are now suggested to the attention
of the reader of the present volume.
All the papers have been refereed, with invaluable help of the Department of Al-
gebra of Moscow State University. The technical job of preparing the manuscripts
for this volume was done by Ilya Bahturin.
The Editor
Table of Contents
Schedule of Talks xi
A. I. Kostrikin
A word about Kurosh 1
A. A. Abramov, V. O. Belash and L. F. Yukhno
Two methods for solving the linear problem of elimination 9
s
I. Agoston, V. Dlab and E. Lukacs
Strictly stratified algebras 17
N. Yu. Anisimov and E. E. Demidov
Randomness: algebraic, statistical and complexity theory aspects 27
V. A. Artamonov
General quantum polynomials 35
A. V. Astrelin, O. D. Golubitsky and E. V. Pankratiev
Gröbner bases and involutive bases 49
Y. Bahturin, A. Giambruno and M. Zaicev
Codimension growth and graded identities 57
R. M. Bryant and A. N. Krasil'nikov
On certain non-finitely based varieties of groups 77
F. Campana
^-connectedness of compact Kahler manifolds, II.
Solvable quotients of Kahler groups 85
A. A. Davydov
Finite groups with the same character tables, Drinfel'd algebras
and Galois algebras 99
R. I. Grigorchuk, W. N. Herfort and P. A. Zalesskii
The profinite completion of certain torsion p-groups 113
M. Grinenko
Birational correspondences of a double cone 125
H. Heineken
Groups with neighborhood conditions for certain lattices 135
viii Table of Contents
N. K. lyudu
Subalgebra membership problem and subalgebra standard basis 137
D. A. Jordan
Graded algebras generated by Eulerian derivatives 145
Y. Kachi and E. Sato
Characterizations of projective spaces and hyperquadrics 155
U. Knauer
Non additive Morita theory. A survey 167
A. I. Kostrikin and A. S. Dzhumadil'daev
Modular Lie algebras: new trends 181
V. S. Kulikov
On generic coverings of the plane 205
V. N. Latyshev
General version of standard bases in linear structures 215
A. I. Lichtman
Division rings generated by group rings and enveloping algebras 227
D. B. Nikolova and B. I. Plotkin
Some notes on universal algebraic geometry 237
D. S. Passman and W. V. Temple
Groups with all irreducible modules of finite degree 263
V. M. Petrogradsky
Schreier's formulae for free Lie algebras, their applications
and asymptotics 281
A. G. Pinus
Conditional terms and their applications 291
Yu. G. Prokhorov
Blow-ups of canonical singularities 301
A. Regev and A. Gouterman
On the growth of identities 319
L. A. Shemetkov
Radical and residual classes of finite groups 331
Table of Contents ix
/. P. Shestakov
Speciality and deformations of algebras 345
T. Vovkivsky
Infinite torsion groups arising as generalizations of the second
Grigorchuk groups 357
V. I. Yanchevskii
Brauer groups of curves and reciprocity law in Brauer groups
of their function fields 379
V. K. Zakharov and A. V. Mikhalev
Mathematical systems 397
