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These notes form an extended version of talks given at the
DMV-seminar 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) "Galois-Module 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. DMV-Seminar 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 p-Sylow 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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