A. Ballester-Bolinches, J. Cossey, S. Y. Madanha , M. C. Pedraza-Aguilera
{"title":"On totally semipermutable products of finite groups","authors":"A. Ballester-Bolinches, J. Cossey, S. Y. Madanha , M. C. Pedraza-Aguilera","doi":"10.1007/s10474-024-01392-4","DOIUrl":null,"url":null,"abstract":"<p>We say a group <i>G</i> = <i>AB</i> is the totally semipermutable product of subgroups <i>A</i> and <i>B</i> if every Sylow subgroup <i>P</i> of <i>A</i> is totally permutable with every Sylow subgroup <i>Q</i> of <i>B</i> whenever <span>\\( \\gcd(|P|,|Q|)=1 \\)</span>. Products of pairwise totally semipermutable subgroups are studied in this article. Let <span>\\( \\mathfrak{U} \\)</span> denote the class of supersoluble groups and <span>\\( \\mathfrak{D} \\)</span> denote the formation of all groups which have an ordered Sylow tower of supersoluble type. We obtain the <span>\\( \\mathfrak{F} \\)</span>-residual of the product from the <span>\\( \\mathfrak{F} \\)</span>-residuals of the pairwise totally semipermutable subgroups when <span>\\( \\mathfrak{F} \\)</span> is a subgroup-closed saturated formation such that <span>\\( \\mathfrak{U}\\subseteq \\mathfrak{F}\\subseteq \\mathfrak{D} \\)</span>.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10474-024-01392-4","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 say a group G = AB is the totally semipermutable product of subgroups A and B if every Sylow subgroup P of A is totally permutable with every Sylow subgroup Q of B whenever \( \gcd(|P|,|Q|)=1 \). Products of pairwise totally semipermutable subgroups are studied in this article. Let \( \mathfrak{U} \) denote the class of supersoluble groups and \( \mathfrak{D} \) denote the formation of all groups which have an ordered Sylow tower of supersoluble type. We obtain the \( \mathfrak{F} \)-residual of the product from the \( \mathfrak{F} \)-residuals of the pairwise totally semipermutable subgroups when \( \mathfrak{F} \) is a subgroup-closed saturated formation such that \( \mathfrak{U}\subseteq \mathfrak{F}\subseteq \mathfrak{D} \).
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.