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The normalizer property for integral group rings of holomorphs of finite groups with trivial center. (English) Zbl 07189508
Summary: Let \(G = \text{Hol}(H)\) be the holomorph of a finite group \(H\). If there is a prime \(q\) dividing \(| H |\) such that every \(q\)-central automorphism of \(H\) is inner and \(Z(H) = 1\), then every Coleman automorphism of \(G\) is inner. In particular, the normalizer property holds for \(G\).
MSC:
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
16S34 Group rings
20C10 Integral representations of finite groups
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