Representation Theory, Group Rings, and Coding Theory.
Isaacs, M.
Representation Theory, Group Rings, and Coding Theory. - 1st ed. - 1 online resource (392 pages) - Contemporary Mathematics ; v.93 . - Contemporary Mathematics .
Intro -- Contents -- Preface -- S.D. Berman (1922-1987): A Biographical Note -- Publications of S. D. Berman -- Ph.D. Students of S.D. Berman -- The S. D. Berman work on coding theory and on theory of threshold functions -- Berman's contributions to group representation over fields -- 1. Introduction -- 2. Counting irreducible and indecomposable representations -- 3. Induced representations -- 4. Effective constructions of representations -- 5. The Schur index -- S. D. Berman's contribution to the theory of integral representations of finite groups -- The work of S. D. Berman on infinite abelian group rings -- Berman's work on units in group rings -- On p-subgroups of finite symmetric and alternating groups -- Parameters of abelian codes in the group algebra KG of G = (a) x (b), aP = bP = 1, p prime, over a finite field K with primitive pth root of unity and related MDS-codes -- Locally cyclic modules over a valuation ring -- On the modules over a real crossed group algebra -- The minimal number of generators of wreath products of nilpotent groups -- Torsion free space groups and permutation lattices for finite groups -- Clifford theory and induction from subgroups -- The isomorphism problem for modular group algebras of groups with large centres -- Zero divisors in group rings: Something old, something new -- The augmentation quotients of finite abelian p-groups -- Free groups in normal subgroups of unit groups and arithmetic groups -- On the Bass-Milnor index of abelian p-groups -- A remark on algebraic geometric codes -- On decomposition of a binomial in a skew polynomial ring -- The associated graded algebra of a group algebra -- On nilpotent and soluble subgroups of linear groups over fields of fractions of enveloping algebras and of group rings, I -- The structure of Go for certain polycyclic group algebras and related algebras. The direct factor problem for modular abelian group algebras -- On the isomorphism of the semi-simple group algebras of the primary abelian groups -- On the canonical irreducible representations of countable locally finite groups and infinite Frobenius group -- Generators of subgroups of U(ZG) -- Connectivity of the finite group and generalized characters.
9780821876817
Berman, S. D. -- (Samuil Davidovich), -- 1922-1987.
Representations of groups.
Group rings.
Coding theory.
Electronic books.
QA174.2 -- .R47 1989eb
512/.2
Representation Theory, Group Rings, and Coding Theory. - 1st ed. - 1 online resource (392 pages) - Contemporary Mathematics ; v.93 . - Contemporary Mathematics .
Intro -- Contents -- Preface -- S.D. Berman (1922-1987): A Biographical Note -- Publications of S. D. Berman -- Ph.D. Students of S.D. Berman -- The S. D. Berman work on coding theory and on theory of threshold functions -- Berman's contributions to group representation over fields -- 1. Introduction -- 2. Counting irreducible and indecomposable representations -- 3. Induced representations -- 4. Effective constructions of representations -- 5. The Schur index -- S. D. Berman's contribution to the theory of integral representations of finite groups -- The work of S. D. Berman on infinite abelian group rings -- Berman's work on units in group rings -- On p-subgroups of finite symmetric and alternating groups -- Parameters of abelian codes in the group algebra KG of G = (a) x (b), aP = bP = 1, p prime, over a finite field K with primitive pth root of unity and related MDS-codes -- Locally cyclic modules over a valuation ring -- On the modules over a real crossed group algebra -- The minimal number of generators of wreath products of nilpotent groups -- Torsion free space groups and permutation lattices for finite groups -- Clifford theory and induction from subgroups -- The isomorphism problem for modular group algebras of groups with large centres -- Zero divisors in group rings: Something old, something new -- The augmentation quotients of finite abelian p-groups -- Free groups in normal subgroups of unit groups and arithmetic groups -- On the Bass-Milnor index of abelian p-groups -- A remark on algebraic geometric codes -- On decomposition of a binomial in a skew polynomial ring -- The associated graded algebra of a group algebra -- On nilpotent and soluble subgroups of linear groups over fields of fractions of enveloping algebras and of group rings, I -- The structure of Go for certain polycyclic group algebras and related algebras. The direct factor problem for modular abelian group algebras -- On the isomorphism of the semi-simple group algebras of the primary abelian groups -- On the canonical irreducible representations of countable locally finite groups and infinite Frobenius group -- Generators of subgroups of U(ZG) -- Connectivity of the finite group and generalized characters.
9780821876817
Berman, S. D. -- (Samuil Davidovich), -- 1922-1987.
Representations of groups.
Group rings.
Coding theory.
Electronic books.
QA174.2 -- .R47 1989eb
512/.2