UID:
almafu_9958354388802883
Umfang:
1 online resource (459p.)
ISBN:
9783110372946
Serie:
De Gruyter Textbook
Inhalt:
This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all details on describing generic constructions of units and their subgroups.
Anmerkung:
Frontmatter --
,
Preface --
,
Contents --
,
1. Units in group rings: an introduction --
,
2. Representations of algebras --
,
3. Wedderburn decomposition of semisimple group algebras --
,
4. Dedekind domains, valuations and orders --
,
5. The group of units of an order --
,
6. Cyclotomic integers --
,
7. Central units --
,
8. Generic units --
,
9. K-theory --
,
10. General linear groups of degree 2 --
,
11. Generators of the unit group of an integral group ring --
,
12. Exceptional simple components --
,
13. Idempotents and central units in group rings --
,
References --
,
Index of Notation --
,
Index
Sprache:
Englisch
DOI:
10.1515/9783110372946
URL:
https://doi.org/10.1515/9783110372946
URL:
https://doi.org/10.1515/9783110372946
