{"title":"Coleman automorphisms of finite groups with semidihedral Sylow 2-subgroups","authors":"R. Aragona","doi":"10.1007/s10474-024-01408-z","DOIUrl":null,"url":null,"abstract":"<div><p>We study some families of finite groups having inner class-preserving\nautomorphisms. In particular, let <i>G</i> be a finite group and <i>S</i> be a\nsemidihedral Sylow 2-subgroup. Then, in both cases when either Sym(4) is not\na homomorphic image of <i>G</i> and <span>\\(Z(S) < Z(G)\\)</span> or <i>G</i> is nilpotent-by-nilpotent, we\nhave that all the Coleman automorphisms of <i>G</i> are inner. As a consequence, these\ngroups satisfy the <i>normalizer problem</i>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"172 2","pages":"413 - 421"},"PeriodicalIF":0.6000,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01408-z.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-024-01408-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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。
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.
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