Contributions to the integral representation theory of groups [Elektronische Ressource] / Martin Hertweck

Contributions to the integral representation theory of groups [Elektronische Ressource] / Martin Hertweck

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Contributions to theintegral representation theory ofgroupsMartin HertweckHabilitationsschrift, approved bythe Faculty of Mathematics and PhysicsUniversity of Stuttgart, 2004Je sais bien que le lecteur n’a pas grand besoin de savoirtout cela, mais j’ai besoin, moi, de le lui dire.Jean-Jacques RousseauLes Confessions { Livre I, 17822000 Mathematics Subject Classiflcation.20C05 Group rings of flnite groups and their modules20C07 rings of inflnite groups and their modules20C10 Integral representations of flnite groups16S34 Group rings16U60 Units, groups of units16U70 Center, normalizer (invariant elements)Keywords and Phrases.group, automorphism, unit group, integral representation theory,isomorphism problem, normalizer problem, Zassenhaus conjectureThis thesis is available as an online publication athttp://elib.uni-stuttgart.de/opusContentsNotation vZusammenfassung (German summary) viiSummary 1I. On the isomorphism problem for integral group rings 161. Local{global considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162. Mazur’s construction adapted to flnite groups . . . . . . . . . . . . . . . . . . 203. Semilocal analysis of the counterexample . . . . . . . . . . . . . . . . . . . . 254. A group-theoretical problem related to the isomorphism problem . . . . . . . 335. Automorphisms of group rings of abelian by nilpotent groups . . . . . . . . . 38II. On the Zassenhaus conjecture 426. Some general observations . . . . . . . . .

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Published 01 January 2004
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