具有自中心化正规子群的有限群的Coleman自同构
Coleman Automorphisms of Finite Groups with a Self-Centralizing Normal Subgroup
摘要:
设G为具有自中心化正规子群N的有限群。在这篇注记中，我们研究了自中心化正规子群N的性质对G的Coleman外自同构群结构的影响，证明了N在某些条件下G的Coleman自同构均为内自同构。这样的Coleman自同构对研究整群环的正规化子问题有着重要的作用。
Abstract:
Let G be a finite group with a self-centered normal subgroup N. In this note, we studied the effects of the properties of the self-centered normal subgroup N on the structure of the Coleman outer automorphism group of G and proved that all Coleman automorphisms of G are inner when N is under some conditions. Such Coleman automorphisms play an important role in the research of normalizer problem for integral group rings.
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