Frobenius Groups And Classical Maximal Orders
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Frobenius Groups and Classical Maximal Orders
Introduction Lemmas on truncated group rings Groups of real quaternions Proof of the classification theorem Frobenius complements with core index 1 Frobenius complements with core index 4 Frobenius complements with core index 12 Frobenius complements with core index 24 Frobenius complements with core index 60 Frobenius complements with core index 120 Counting Frobenius complements Maximal orders Isomorphism classes of Frobenius groups with Abelian Frobenius kernel Concrete constructions of Frobenius groups Counting Frobenius groups with Abelian Frobenius kernel Isomorphism invariants for Frobenius complements Schur indices and finite subgroups of division rings Bibliography
Frobenius Groups and Classical Maximal Orders
Introduction Lemmas on truncated group rings Groups of real quaternions Proof of the classification theorem Frobenius complements with core index 1 Frobenius complements with core index 4 Frobenius complements with core index 12 Frobenius complements with core index 24 Frobenius complements with core index 60 Frobenius complements with core index 120 Counting Frobenius complements Maximal orders Isomorphism classes of Frobenius groups with Abelian Frobenius kernel Concrete constructions of Frobenius groups Counting Frobenius groups with Abelian Frobenius kernel Isomorphism invariants for Frobenius complements Schur indices and finite subgroups of division rings Bibliography.
Orders and Generic Constructions of Units
Author: Eric Jespers
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2015-11-13
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. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.