具有半面体 Sylow 2 子群的有限群的 Coleman 自形变

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2024-03-13 DOI:10.1007/s10474-024-01408-z

R. Aragona

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引用次数: 0

摘要

我们研究有限群中一些具有内类保留自变的群族。特别地，让 G 是一个有限群，S 是一个半面体 Sylow 2 子群。那么，在这两种情况下，当 Sym(4) 不是 G 的同构像且（Z(S) < Z(G)）或 G 是逐个零potent 时，我们就会得到 G 的所有科尔曼自变分都是内自变分。因此，这些群满足归一化问题。

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Coleman automorphisms of finite groups with semidihedral Sylow 2-subgroups

We study some families of finite groups having inner class-preserving automorphisms. In particular, let G be a finite group and S be a semidihedral Sylow 2-subgroup. Then, in both cases when either Sym(4) is not a homomorphic image of G and \(Z(S) < Z(G)\) or G is nilpotent-by-nilpotent, we have that all the Coleman automorphisms of G are inner. As a consequence, these groups satisfy the normalizer problem.

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.