By a remark made earlier (Remark (l), p.35), all free groups have cohomological dimension <s l. ... The general group-theoretic significance of finite 121 cohomological dimension is still an almost untouched problem. The l2O $8.1.

This report was first published (in French) by Benjamin. For this new English edition, the author added Tate's local duality, written up from letters which John Tate sent to Lang in 1958 - 1959.

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 3540611819

Category: Mathematics

Page: 236

View: 325

The book is a mostly translated reprint of a report on cohomology of groups from the 1950s and 1960s, originally written as background for the Artin-Tate notes on class field theory, following the cohomological approach. This report was first published (in French) by Benjamin. For this new English edition, the author added Tate's local duality, written up from letters which John Tate sent to Lang in 1958 - 1959. Except for this last item, which requires more substantial background in algebraic geometry and especially abelian varieties, the rest of the book is basically elementary, depending only on standard homological algebra at the level of first year graduate students.

This is not an account of the cohomology theory of groups as such . I have tried rather to cut a path across this theory past as many group theoretical points of interest as possible . The subject is group theory with a cohomological ...

[12] [13] [14] [15] [16] [17] [18] [19] [20] [21 [22] [23] [24] (25 K. W. Gruenberg, Cohomological topics in Group Theory, Lecture Notes in Mathematics, Vol. 143, Springer, Berlin (1970). P. Hall, Finiteness conditions for soluble ...

Author: Kai N. Cheng

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110848397

Category: Mathematics

Page: 603

View: 898

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Groups with homological duality generalizing Poincaré duality, Invent. Math. ... Arithmetic properties of linear algebraic groups, m Int. Congress Math. , Stockholm (1962), 10-22. ... Cohomological topics in group theory, Lect.

Author: C. T. C. Wall

Publisher: Cambridge University Press

ISBN: 9780521227292

Category: Mathematics

Page: 409

View: 414

Eminent mathematicians have presented papers on homological and combinatorial techniques in group theory. The lectures are aimed at presenting in a unified way new developments in the area.

R. Godement ( 1958 ) , Topologie algébrique et théorie des faisceaux , Hermann , Paris , 1958 . 0. Goldman ( 1961 ) , Determinants in ... K. W. Gruenberg ( 1970 ) , Cohomological topics in group theory , Lecture Notes in Math .

Author: Kenneth S. Brown

Publisher: Springer Science & Business Media

ISBN: 9781468493276

Category: Mathematics

Page: 306

View: 562

Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.

P. Fong, R.J. Milgram, On the geometry and cohomology of the simple groups G2(q) and *D4 (q), preprint, Stanford University ... K. Gruenberg, Cohomological Topics in Group Theory, Lecture Notes in Mathematics 143, Springer-Verlag 1970.

Author: Alejandro Adem

Publisher: Springer Science & Business Media

ISBN: 9783662062807

Category: Mathematics

Page: 324

View: 463

Some Historical Background This book deals with the cohomology of groups, particularly finite ones. Historically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homo logical algebra and algebraic K-theory. It arose primarily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work ofH. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the meanings of the low dimensional homology groups of a space X. For example, if the universal cover of X was three connected, it was known that H2(X; A. ) depends only on the fundamental group of X. Group cohomology initially appeared to explain this dependence. In number theory, group cohomology arose as a natural device for describing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field. It also arose naturally in the study of group extensions, N

Lg-cohomology and group cohomology. ... Vanishing theorems and conjectures for the £2-homology of right-angled Coxeter groups. Geom. Topol., 5:7G74 (electronic), 2001. P. de la Harpe. Topics in geometric group theory.

Author: Martin R. Bridson

Publisher: Cambridge University Press

ISBN: 9780521757249

Category: Mathematics

Page: 331

View: 444

An extended tour through a selection of the most important trends in modern geometric group theory.

A generalization of the transfer map in the cohomology of groups . Trans . Amer . Math . Soc . ... On the Chern classes of representations of finite groups . Trans . Amer . Math . Soc . ... Cohomological topics in group theory .

Author: D. J. Benson

Publisher: Cambridge University Press

ISBN: 0521636523

Category: Mathematics

Page: 296

View: 114

A further introduction to modern developments in the representation theory of finite groups and associative algebras.