{"title":"正则分支群的Hausdorff维数计算算法","authors":"Jorge Fariña-Asategui","doi":"10.1016/j.jaca.2025.100037","DOIUrl":null,"url":null,"abstract":"<div><div>An explicit algorithm is given for the computation of the Hausdorff dimension of the closure of a regular branch group in terms of an arbitrary branch structure. We implement this algorithm in GAP and apply it to a family of GGS-groups acting on the 4-adic tree.</div></div>","PeriodicalId":100767,"journal":{"name":"Journal of Computational Algebra","volume":"15 ","pages":"Article 100037"},"PeriodicalIF":0.0000,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An algorithm to compute the Hausdorff dimension of regular branch groups\",\"authors\":\"Jorge Fariña-Asategui\",\"doi\":\"10.1016/j.jaca.2025.100037\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>An explicit algorithm is given for the computation of the Hausdorff dimension of the closure of a regular branch group in terms of an arbitrary branch structure. We implement this algorithm in GAP and apply it to a family of GGS-groups acting on the 4-adic tree.</div></div>\",\"PeriodicalId\":100767,\"journal\":{\"name\":\"Journal of Computational Algebra\",\"volume\":\"15 \",\"pages\":\"Article 100037\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2025-06-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2772827725000087\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Algebra","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2772827725000087","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An algorithm to compute the Hausdorff dimension of regular branch groups
An explicit algorithm is given for the computation of the Hausdorff dimension of the closure of a regular branch group in terms of an arbitrary branch structure. We implement this algorithm in GAP and apply it to a family of GGS-groups acting on the 4-adic tree.
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