{"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":null,"pages":null},"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\":null,\"pages\":null},\"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}
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, bg〉, where g ∈ G, are finite, then G = A λ CG(i) is a Frobenius group with Abelian kernel A and complement CG(i) whose elementary Abelian subgroups are all cyclic.
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.
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