{"title":"有限单群饱和的周期群L4（q）","authors":"W. Guo, D. V. Lytkina, V. D. Mazurov","doi":"10.1007/s10469-022-09662-2","DOIUrl":null,"url":null,"abstract":"<div><div><p>If M is a set of finite groups, then a group G is said to be saturated with the set M (saturated with groups in M) if every finite subgroup of G is contained in a subgroup isomorphic to some element of M. It is proved that a periodic group with locally finite centralizers of involutions, which is saturated with a set consisting of groups L<sub>4</sub>(q), where q is odd, is isomorphic to L<sub>4</sub>(F) for a suitable field F of odd characteristic.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"60 6","pages":"360 - 365"},"PeriodicalIF":0.6000,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Periodic Groups Saturated with Finite Simple Groups L4(q)\",\"authors\":\"W. Guo, D. V. Lytkina, V. D. Mazurov\",\"doi\":\"10.1007/s10469-022-09662-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div><p>If M is a set of finite groups, then a group G is said to be saturated with the set M (saturated with groups in M) if every finite subgroup of G is contained in a subgroup isomorphic to some element of M. It is proved that a periodic group with locally finite centralizers of involutions, which is saturated with a set consisting of groups L<sub>4</sub>(q), where q is odd, is isomorphic to L<sub>4</sub>(F) for a suitable field F of odd characteristic.</p></div></div>\",\"PeriodicalId\":7422,\"journal\":{\"name\":\"Algebra and Logic\",\"volume\":\"60 6\",\"pages\":\"360 - 365\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-06-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra and Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10469-022-09662-2\",\"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/s10469-022-09662-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"LOGIC","Score":null,"Total":0}
Periodic Groups Saturated with Finite Simple Groups L4(q)
If M is a set of finite groups, then a group G is said to be saturated with the set M (saturated with groups in M) if every finite subgroup of G is contained in a subgroup isomorphic to some element of M. It is proved that a periodic group with locally finite centralizers of involutions, which is saturated with a set consisting of groups L4(q), where q is odd, is isomorphic to L4(F) for a suitable field F of odd characteristic.
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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