S. E. ©MR, Issn, Ñèáèðñêèå Ýëåêòðîííûå, ÌÀÒÅÌÀÒÈ×ÅÑÊÈÅ ÈÇÂÅÑÒÈß, N. T. Kogabaev
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{"title":"On closure of configurations in freely generated projective planes","authors":"S. E. ©MR, Issn, Ñèáèðñêèå Ýëåêòðîííûå, ÌÀÒÅÌÀÒÈ×ÅÑÊÈÅ ÈÇÂÅÑÒÈß, N. T. Kogabaev","doi":"10.33048/semi.2021.18.025","DOIUrl":null,"url":null,"abstract":"Let F be an arbitrary freely generated projective plane. Based on Shirshov's combinatorial method, we introduce the notion of a reduced con guration in F . We prove that for every subplane P generated in F by some con guration B, there is a reduced con guration B′ such that P is freely generated by B′.","PeriodicalId":45858,"journal":{"name":"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya","volume":"1 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33048/semi.2021.18.025","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
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自由生成投影平面中构型的闭包
设F是一个任意自由生成的投影平面。在Shirshov组合方法的基础上,引入了简化构型的概念。我们证明了对于F中由某个构型B生成的每一个子平面P,存在一个简化构型B ',使得P可以由B '自由生成。
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