Cyclic cellularity and active sums

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• 作者：Nadia Romero
• 关键词：20F55 ; 20F99 ; 55P60 ; 55P99 ; Cellular group ; Active sum
• 刊名：Archiv der Mathematik
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：105
• 期：4
• 页码：307-311
• 全文大小：411 KB
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  8.Tomás F.: Un análogo de suma directa para sistemas de subgrupos normales, Anales del Instituto de Matemáticas UNAM 13, 161-86 (1973)
  
• 作者单位：Nadia Romero (1)
  
  1. Departamento de Matemáticas, Universidad de Guanajuato, Guanajuato, Mexico
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8938

文摘

Let G be a group, and let \({\mathcal{F}}\) be a family of subgroups of G closed under conjugation. For a positive integer n, let C _n denote a cyclic group of order n. We show that if there exists an integer n such that every group in \({\mathcal{F}}\) is C _n -cellular and has finite exponent diving n, then the active sum S of \({\mathcal{F}}\) is C _n -cellular. We obtain a couple of interesting consequences of this result, using results about cellularity. Finally, we give different proofs of the facts that Coxeter groups are C ₂-cellular and that many groups of the form \({\mathrm{SL}(n, q)}\) for n ?3 are C ₃-cellular. Keywords Cellular group Active sum