Preface This volume is dedicated to the memory of the outstanding Soviet math- ematicianS. D. Berman (1922-1987). S. D. Berman worked, for the most part, in representation theory, group rings and coding theory. His important mathematical contributions are dis- cussed here in a number of review articles. First B. N. Gartshtein and I. I. Grushko describe Berman's achievements in coding theory, including his pioneering work on abelian codes and his results on the theory of threshold functions, produced during the last ten years of his life. G. Karpilovskii considers Berman's contributions to the representation theory of groups over fields. The article by A. I. Lichtman discusses Berman's work on integral rep- resentations of groups, especially his fundamental theorem on groups of finite representation type, proved in the period 1959-1962. Next W. May describes Berman's accomplishments in infinite abelian group rings, in particular the results of his famous Debrecen paper ( 1967). The article by R. Sandling is devoted to Berman's fundamental results on units in integral group rings. Finally the biographical sketch of S.D. Berman is written by A. I. Lichtman. This volume also contains twenty-two research articles in the areas of S. D. Berman's major interests. These papers are presented by mathemati- cians from many countries: United States, Soviet Union, England, Canada, Australia, Hungary, Bulgaria, South Africa-a sign of honor from the inter- national mathematical community to a mathematician who contributed so much. We would like to thank all the authors, the editors of the American Math- ematical Society and all the people who made this collection possible. M. Isaacs, University of Wisconsin-Madison A. Lichtman, University of Wisconsin-Parkside D. Passman, University of Wisconsin-Madison S. Sehgal, University of Alberta, Edmonton, Canada N. J. A. Sloane, AT & T Bell Labs H. Zassenhaus, Ohio State University XV
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