{"title":"由有限 $p$-automata 定义的自由群","authors":"A. Krenevych, A. Oliynyk","doi":"10.15421/242314","DOIUrl":null,"url":null,"abstract":"For every odd prime $p$ we construct two $p$-automata with 14 inner states and prove that the group generated by 2 automaton permutations defined at their states is a free group of rank 2.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"12 13","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Free groups defined by finite $p$-automata\",\"authors\":\"A. Krenevych, A. Oliynyk\",\"doi\":\"10.15421/242314\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For every odd prime $p$ we construct two $p$-automata with 14 inner states and prove that the group generated by 2 automaton permutations defined at their states is a free group of rank 2.\",\"PeriodicalId\":52827,\"journal\":{\"name\":\"Researches in Mathematics\",\"volume\":\"12 13\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Researches in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15421/242314\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Researches in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15421/242314","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
For every odd prime $p$ we construct two $p$-automata with 14 inner states and prove that the group generated by 2 automaton permutations defined at their states is a free group of rank 2.
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