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Representation Theory, Group Rings, and Coding Theory
Edited by: M. Isaacs, A. Lichtman, D. Passman, S. Sehgal, N. J. A. Sloane, and H. Zassenhaus
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Contemporary Mathematics
1989; 357 pp; softcover
Volume: 93
ISBN-10: 0-8218-5098-9
ISBN-13: 978-0-8218-5098-5
List Price: US$73 Member Price: US$58.40
Order Code: CONM/93

This volume is dedicated to the memory of the Soviet mathematician S. D. Berman (1922-1987). Berman's work--for the most part in representation theory, group rings, and coding theory--is discussed here in a number of review articles. Among the topics covered are Berman's achievements in coding theory, including his pioneering work on abelian codes and his results on the theory of threshold functions. Also discussed are his contributions to the representation theory of groups over fields, his work on integral representations of groups, his accomplishments in infinite abelian group rings, and his fundamental results on units in integral group rings. In addition, there are 22 research articles written by an international group of researchers in areas of Berman's major interest.

• B. N. Gartshtein and I. I. Grushko -- The S. D. Berman work on coding theory and on theory of threshold functions
• G. Karpilovsky -- Berman's contributions to group representations over fields
• A. I. Lichtman -- S. D. Berman's contribution to the theory of integral representations of finite groups
• W. May -- The work of S. D. Berman on infinite abelian group rings
• R. Sandling -- Berman's work on units in group rings
• J. G. Berkovic -- On $$p$$-subgroups of finite symmetric and alternating groups
• S. D. Berman and N. I. Vishnyakova -- Locally cyclic modules over a valuation ring
• K. Buzási -- On the modules over a real crossed group algebra
• K. Buzási and L. G. Kovács -- The minimal number of generators of wreath products of nilpotent groups
• G. Cliff and A. Weiss -- Torsion free space groups and permutation lattices for finite groups
• E. C. Dade -- Clifford theory and induction from subgroups
• V. Drensky -- The isomorphism problem for modular group algebras of groups with large centres
• D. R. Farkas and P. A. Linell -- Zero divisors in group rings: something old, something new
• A. W. Hales and I. B. S. Passi -- The augmentation quotients of finite abelian $$p$$-groups
• B. Hartley -- Free groups in normal subgroups of unit groups and arithmetic groups
• K. Hoechsmann -- On the Bass-Milnor index of abelian $$p$$-groups
• G. L. Katsman and M. A. Tsafsman -- A remark on algebraic geometric codes
• E. S. Kerer -- On decomposition of a binomial in a skew polynomial ring
• L. Krop -- The associated graded algebra of a group algebra
• A. I. Lichtman -- On nilpotent and soluble subgroups of linear groups over fields of fractions of enveloping algebras and of group rings, I
• M. Lorenz and D. S. Passman -- The structure of $$G_0$$ for certain polycyclic group algebras and related algebras
• W. May -- The direct factor problem for modular abelian group algebras
• T. Z. Mollov -- On the isomorphism of the semi-simple group algebras of the primary abelian groups
• S. I. Ostrovskaya -- On the canonical irreducible representations of countable locally finite groups and infinite Frobenius group
• J. Ritter and S. K. Sehgal -- Generators of subgroups of $$U(\Bbb ZG)$$
• E. M. Žmud -- Connectivity of the finite group and generalized characters