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Projective representations of finite groups
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ISBN: 0824773136 Year: 1985 Volume: vol 94 Publisher: New York Basel M. Dekker

The Jacobson radical of group algebras
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ISBN: 0444701907 9780444701909 9780080872469 0080872468 1281798002 9781281798008 9786611798000 Year: 1987 Volume: 135 Publisher: Amsterdam New York New York, N.Y., U.S.A. North-Holland Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.

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Let G be a finite group and let F be a field. It is well known that linear representations of G over F can be interpreted as modules over the group algebra FG. Thus the investigation of ring-theoretic structure of the Jacobson radical J(FG) of FG is of fundamental importance. During the last two decades the subject has been pursued by a number of researchers and many interesting results have been obtained. This volume examines these results.The main body of the theory is presented, giving the central ideas, the basic results and the fundamental methods. It is assumed that the reader ha

The algebraic structure of crossed products
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ISBN: 0444702393 9780444702395 9780080872537 0080872530 128179807X 9781281798077 9786611798079 Year: 1987 Volume: 142 118 Publisher: Amsterdam New York New York, N.Y., U.S.A. North-Holland Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.

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In the past 15 years, the theory of crossed products has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings.The purpose of this monograph is to give, in a self-contained manner, an up-to-date account of various aspects of this development, in an effort to convey a comprehensive picture of the current state of the subject. It is assumed that the reader has had the equivalent of a standard first-year graduate course, thus familiarity with basic ring-theoretic and g

Field theory : classical foundations and multiplicative groups
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ISBN: 0824780299 Year: 1988 Volume: vol 120 Publisher: New York Basel M. Dekker

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Book
Commutative group algebras
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ISBN: 0824719182 Year: 1983 Publisher: New York (N.Y.): Dekker

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Group representations.
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ISBN: 128216791X 9786612167911 0080872913 044487433X 9780080872919 Year: 1994 Publisher: Amsterdam London North-Holland

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This third volume can be roughly divided into two parts. The first part is devoted to the investigation of various properties of projective characters. Special attention is drawn to spin representations and their character tables and to various correspondences for projective characters. Among other topics, projective Schur index and projective representations of abelian groups are covered. The last topic is investigated by introducing a symplectic geometry on finite abelian groups. The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theo


Book
Induced modules over group algebras
Author:
ISBN: 1281782858 9786611782856 0080872727 0444884149 Year: 1990 Publisher: Amsterdam ; New York : New York, N.Y., U.S.A. : North-Holland ; Distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.,

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In 1898 Frobenius discovered a construction which, in present terminology, associates with every module of a subgroup the induced module of a group. This construction proved to be of fundamental importance and is one of the basic tools in the entire theory of group representations.This monograph is designed for research mathematicians and advanced graduate students and gives a picture of the general theory of induced modules as it exists at present. Much of the material has until now been available only in research articles. The approach is not intended to be encyclopedic, rather each

Clifford theory for group representations
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ISBN: 1281790575 9786611790578 0080872670 0444873775 9780444873774 9780080872674 9781281790576 Year: 1989 Publisher: Amsterdam New York New York, N.Y., U.S.A. North-Holland Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.

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Let N be a normal subgroup of a finite group G and let F be a field. An important method for constructing irreducible FG-modules consists of the application (perhaps repeated) of three basic operations: (i) restriction to FN. (ii) extension from FN. (iii) induction from FN. This is the `Clifford Theory' developed by Clifford in 1937. In the past twenty years, the theory has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings and crossed products.The purpos


Book
Group and semigroup rings
Author:
ISBN: 0444700439 9786611797829 1281797820 0080872379 9780444700438 9780080872377 9781281797827 6611797823 Year: 1986 Publisher: Amsterdam New York New York, N.Y., U.S.A. North-Holland Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.

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A broad range of topics is covered here, including commutative monoid rings, the Jacobson radical of semigroup rings, blocks of modular group algebras, nilpotency index of the radical of group algebras, the isomorphism problem for group rings, inverse semigroup algebras and the Picard group of an abelian group ring. The survey lectures provide an up-to-date account of the current state of the subject and form a comprehensive introduction for intending researchers.

Group representations.
Author:
ISBN: 044488632X 9786613837660 1283525216 0080872867 9781483295091 1483295095 9780444886323 9780444533289 0444533281 9780444887269 0444887261 9780444874337 044487433X 9780444533302 0444533303 9780444891082 0444891080 9780444533319 0444533311 9780444892614 0444892613 9780444530462 0444530460 9781483295107 1483295109 Year: 1996 Volume: 175 Publisher: Amsterdam

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