Group Rings and Class Groups (Oberwolfach Seminars, 18),Used

Group Rings and Class Groups (Oberwolfach Seminars, 18),Used

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These notes form an extended version of talks given at the DMVseminar in Giinzburg, September 1990. The seminar consisted of two parts: 1) "The isomorphism problem for integral group rings", with the main talks given by K. W. Roggenkamp and shorter contributions by W.Kimmerle, J.llitter and A. Zimmermann (Part 1). 2) "GaloisModule structure", with the main talks given by M.Taylor and shorter contributions by N.Byott (Part 2). We greatly appreciate the opportunity, given us by the DMV to hold this seminar. DMVSeminar Part 1 Group Rings: Units and the Isomorphism Problem K. W. Roggenkamp with contributions by W. Kimmerle and A. Zimmermann Contents 3 Table of Contents I Some general facts ... 7 1 Ring reduction to PID . 7 2 Modules ........ . 7 II Some notes on representation theory 9 1 Blocks .................. . 9 2 Normalizers of pSylow subgroups of group bases 11 3 Cohomology rings 12 Profinite groups .. . . . . . . . . 13 4 III The leading coefficient of units 15 IV Class sum correspondence ... . . . . . . . . . . . .. . . 21 .

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