偶数阶补的有限Frobenius群饱和群

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2022-05-05 DOI:10.1007/s10469-022-09664-0

B. E. Durakov

{"title":"偶数阶补的有限Frobenius群饱和群","authors":"B. E. Durakov","doi":"10.1007/s10469-022-09664-0","DOIUrl":null,"url":null,"abstract":"<div><div><p>We prove a theorem stating the following. Let G be a periodic group saturated with finite Frobenius groups with complements of even order, and let i be an involution of G. If, for some elements a, b ∈ G with the condition |a| · |b| > 4, all subgroups 〈<i>a</i>, <i>b</i><sup><i>g</i></sup>〉, where g ∈ G, are finite, then G = A λ C<sub>G</sub>(i) is a Frobenius group with Abelian kernel A and complement C<sub>G</sub>(i) whose elementary Abelian subgroups are all cyclic.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"60 6","pages":"375 - 379"},"PeriodicalIF":0.4000,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Groups Saturated with Finite Frobenius Groups with Complements of Even Order\",\"authors\":\"B. E. Durakov\",\"doi\":\"10.1007/s10469-022-09664-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div><p>We prove a theorem stating the following. Let G be a periodic group saturated with finite Frobenius groups with complements of even order, and let i be an involution of G. If, for some elements a, b ∈ G with the condition |a| · |b| > 4, all subgroups 〈<i>a</i>, <i>b</i><sup><i>g</i></sup>〉, where g ∈ G, are finite, then G = A λ C<sub>G</sub>(i) is a Frobenius group with Abelian kernel A and complement C<sub>G</sub>(i) whose elementary Abelian subgroups are all cyclic.</p></div></div>\",\"PeriodicalId\":7422,\"journal\":{\"name\":\"Algebra and Logic\",\"volume\":\"60 6\",\"pages\":\"375 - 379\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-05-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra and Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10469-022-09664-0\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra and Logic","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10469-022-09664-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"LOGIC","Score":null,"Total":0}

引用次数: 1

摘要

我们证明了一个定理，陈述如下。设G是由具有偶数阶补的有限Frobenius群饱和的周期群，并且设i是G的对合。如果对于某些元素a，b∈G，条件为|a|·|b|>；4、所有子群〈a， bg〉，其中g∈g是有限的，则g=AλCG（i）是具有阿贝尔核A和补码CG（i）的Frobenius群，其初等阿贝尔子群都是循环的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Groups Saturated with Finite Frobenius Groups with Complements of Even Order

We prove a theorem stating the following. Let G be a periodic group saturated with finite Frobenius groups with complements of even order, and let i be an involution of G. If, for some elements a, b ∈ G with the condition |a| · |b| > 4, all subgroups 〈a, b^g〉, where g ∈ G, are finite, then G = A λ C_G(i) is a Frobenius group with Abelian kernel A and complement C_G(i) whose elementary Abelian subgroups are all cyclic.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.