{"title":"轨道同构骨架群","authors":"Subhrajyoti Saha","doi":"10.12958/adm1886","DOIUrl":null,"url":null,"abstract":"Recent development in the classification of p-groups often concentrate on the coclass graph G(p,r) associated with the finitep-groups coclassr, specially on periodicity results on these graphs. In particular, the structure of the subgraph inducedby ‘skeleton groups’ is of notable interest. Given their importance, in this paper, we investigate periodicity results of skeleton groups. Our results concentrate on the skeleton groups in G(p,1). We find a family of skeleton groups in G(7,1) whose 6-step parent is not aperiodic parent. This shows that the periodicity results available inthe current literature for primes p≡5 mod 6 do not hold for the primes p≡1 mod 6. We also improve a known periodicity result in a special case of skeleton groups.","PeriodicalId":364397,"journal":{"name":"Algebra and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Orbit isomorphic skeleton groups\",\"authors\":\"Subhrajyoti Saha\",\"doi\":\"10.12958/adm1886\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Recent development in the classification of p-groups often concentrate on the coclass graph G(p,r) associated with the finitep-groups coclassr, specially on periodicity results on these graphs. In particular, the structure of the subgraph inducedby ‘skeleton groups’ is of notable interest. Given their importance, in this paper, we investigate periodicity results of skeleton groups. Our results concentrate on the skeleton groups in G(p,1). We find a family of skeleton groups in G(7,1) whose 6-step parent is not aperiodic parent. This shows that the periodicity results available inthe current literature for primes p≡5 mod 6 do not hold for the primes p≡1 mod 6. We also improve a known periodicity result in a special case of skeleton groups.\",\"PeriodicalId\":364397,\"journal\":{\"name\":\"Algebra and Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra and Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12958/adm1886\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra and Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12958/adm1886","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
最近在p群分类方面的进展通常集中在与有限群共类相关的协类图G(p,r)上,特别是在这些图的周期性结果上。特别是,由“骨架群”引起的子图结构值得注意。鉴于它们的重要性,本文研究了骨架群的周期性结果。我们的结果集中在G(p,1)中的骨架群上。我们在G(7,1)中发现了一个六步亲本不是非周期亲本的骨架群家族。这表明目前文献中关于素数p≡5 mod 6的周期性结果并不适用于素数p≡1 mod 6。我们还改进了一个已知的骨架群的特殊情况下的周期性结果。
Recent development in the classification of p-groups often concentrate on the coclass graph G(p,r) associated with the finitep-groups coclassr, specially on periodicity results on these graphs. In particular, the structure of the subgraph inducedby ‘skeleton groups’ is of notable interest. Given their importance, in this paper, we investigate periodicity results of skeleton groups. Our results concentrate on the skeleton groups in G(p,1). We find a family of skeleton groups in G(7,1) whose 6-step parent is not aperiodic parent. This shows that the periodicity results available inthe current literature for primes p≡5 mod 6 do not hold for the primes p≡1 mod 6. We also improve a known periodicity result in a special case of skeleton groups.