On isomorphisms between centers of integral group rings of finite groups期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On isomorphisms between centers of integral group rings of finite groups

Authors:	Martin Hertweck

Affiliation:	Universität Stuttgart, Fachbereich Mathematik, IGT, 70569 Stuttgart, Germany

Abstract:	For finite nilpotent groups and $G^{prime}$ , and a -adapted ring (the rational integers, for example), it is shown that any isomorphism between the centers of the group rings and $SG^{prime}$ is monomial, i.e., maps class sums in to class sums in $SG^{prime}$ up to multiplication with roots of unity. As a consequence, and $G^{prime}$ have identical character tables if and only if the centers of their integral group rings and $mathbb{Z} G^{prime}$ are isomorphic. In the course of the proof, a new proof of the class sum correspondence is given.

Keywords:	$p$-group integral group ring class sum correspondence

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