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Let G be a finite group and Out Col(G) the Coleman outer automorphism group of G(for the definition, see below). The question whether OutCol(G) is a p′-group naturally arises from the study of the normalizer problem for integral group rings, where p is a prime. In this article, some sufficient conditions for OutCol(G) to be a p′-group are obtained. Our results generalize some well-known theorems.  相似文献
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Let π be a set of primes. Isaacs established the π-theory of characters, which generalizes the theory of Brauer modular characters. Motivated by Isaacs's work, we introduce the definition of Mπ-groups and provide a characterization of Mπ-groups.  相似文献
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Let G be a finite group with a unique nontrivial normal subgroup. It is shown that every Coleman automorphism of G is an inner automorphism.  相似文献
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设$H$是有限群$G$的一个子群,若对任意$g\in G$, $H\cap H^g=1$或者$H$,则称$H$为TI-子群. 设$G$是一个所有二极大子群为TI-子群的有限群,本文证明了$G$的每个类保持Coleman自同构是内自同构. 作为本结果的一个直接推论,得到了这样的群$G$有正规化子性质.  相似文献
5.
Let G be a finite group and Outcoz(G) the Coleman outer automorphism group of G(for the definition, see below). The question whether Outcol(G) is a p′-group naturally arises from the study of the normalizer problem for integral group rings, where p is a prime. In this article, some sufficient conditions for OutCol(G) to be a p'-group are obtained. Our results generalize some well-known theorems.  相似文献
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Let H be the holomorph of a finite group G. It is proved that every Coleman automorphism of H is inner whenever G is either completely reducible or almost simple; in particular, this is the case when G is either characteristically simple or simple. As an application, we obtain the normalizer the conjecture holds for integral group rings of holomorphs of such groups in question.  相似文献
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