一些特殊的共点行动及其结果

Pub Date : 2024-07-03 DOI:10.1016/j.jpaa.2024.107764

Gülı̇n Ercan , İsmaı̇l Ş. Güloğlu , M. Yası̇r Kizmaz , Danila O. Revin

{"title":"一些特殊的共点行动及其结果","authors":"Gülı̇n Ercan , İsmaı̇l Ş. Güloğlu , M. Yası̇r Kizmaz , Danila O. Revin","doi":"10.1016/j.jpaa.2024.107764","DOIUrl":null,"url":null,"abstract":"<div>Let a group A act on the group G coprimely. Suppose that the order of the fixed point subgroup <math><msub><mrow><mi>C</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math> is not divisible by an arbitrary but fixed prime p. In the present paper we determine bounds for the p-length of the group G in terms of the order of A, and investigate how some A-invariant p-subgroups are embedded in G under various additional assumptions.</div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some special coprime actions and their consequences\",\"authors\":\"Gülı̇n Ercan , İsmaı̇l Ş. Güloğlu , M. Yası̇r Kizmaz , Danila O. Revin\",\"doi\":\"10.1016/j.jpaa.2024.107764\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>Let a group A act on the group G coprimely. Suppose that the order of the fixed point subgroup <math><msub><mrow><mi>C</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math> is not divisible by an arbitrary but fixed prime p. In the present paper we determine bounds for the p-length of the group G in terms of the order of A, and investigate how some A-invariant p-subgroups are embedded in G under various additional assumptions.</div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022404924001610\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404924001610","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

让一个群 A 共同作用于群 G。假设定点子群 CG(A) 的阶不能被任意但固定的素数 p 整除。在本文中，我们根据 A 的阶确定了群 G 的 p 长度的边界，并研究了在各种附加假设下，一些 A 不变的 p 子群是如何嵌入 G 的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

Some special coprime actions and their consequences

Let a group A act on the group G coprimely. Suppose that the order of the fixed point subgroup $C_{G} (A)$ is not divisible by an arbitrary but fixed prime p. In the present paper we determine bounds for the p-length of the group G in terms of the order of A, and investigate how some A-invariant p-subgroups are embedded in G under various additional assumptions.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助