收藏本站
收藏 | 手机打开
二维码
手机客户端打开本文

Some Properties of Two Classes of Finite Groups

Farai.A.Abdunabi  
【摘要】:The groups that consist of non-bijective transformations on a non-empty set A where the binary operation on a group G is the composition of transformations have been recently given. A permutation group on a set A is a group which consisting of bijections from A to A with respect to compositions of mappings have been made in the framework of the abstract algebra approach. In this thesis, we show that there exist some groups which consist of non-bijective transformations on a non-empty set A. We introduce the maximal order of these groups (that consisting of transformations on a non-empty set A and the group has no bijection as its element). We found the order of these groups is not greater than (n-1)! and any kind of these group isomorphic to a permutation group on a quotient set of A with respect to an equivalence relation on A. Moreover, we answer the question that if G=UV with U, V are subnormal in G then it holds that the maximal normal χ-subgroup of G is equal UχVχ. We found if p is a prime and take the SHP-class X to be the class of all finite p-group, then for any finite group Gχ will be OP(G). We prove that U, V are both subnormal in G and Op(G)=〈y〉and OP(U)=OP(V)= 1. In particular, OP(G)≠Op(U)Op(V) if p and q are two primes such that q≡1(mod/p) with N is a cyclic group of order q, H is an elementary abelian group of order p2, and〈x〉 act on N faithfully and〈y〉act on N trivially on the semi-direct product of N and Hwhere U= N(x)and V=〈xy〉. In addition, we consider the groups that consist of non-bijective transformations on a non-empty set A by using the fixed points. We found the order of these groups is equal of the order of orbit multiply order of stabilizer for any fixed points.We divide the thesis to four chapters. First chapter, study a new group that consists of non-bijective transformations on a non-empty set A where the binary operation on group G. These new groups are given by examples. And, we consider the maximal order of a group consisting of transformations on a non-empty set A and the group has no bijections as it is elements. The second chapter, we review some basic concepts in a finite group such a binary operation on a group G and some other definitions. Moreover, we study the symmetric groups and the proof of theorems and lemmas that have used in this thesis. In the third chapter, we consider new groups which consists of non-bijective transformations on a non-empty set A and introduce the maximal order of groups which consist of non-bijective transformations on a non-empty set A of order n where the binary operation on a group G as a new result. The maximal order of these groups is (n-1)!. We apply these groups to study some properties of two classes of finite groups. Fourth chapter, devoted to study our groups by using the fixed points.


知网文化
【相似文献】
中国期刊全文数据库 前20条
1 贺继刚;;Efficacy of subgroup mouse bone mesenchymal stem cells on mobilizing autologous cardiac stem cells and repairing ischemic myocardial tissue[J];China Medical Abstracts(Internal Medicine);2013年02期
2 NGU Min Hui;WONG Kok Bin;WONG Peng Choon;;Basic subgroup and Reid's theorem[J];Science China(Mathematics);2011年10期
3 ;On X-s-Permutable Subgroups of a Finite Group[J];数学研究与评论;2010年05期
4 SHUM Kar Ping;SKIBA Alexander N.;;On solubility and supersolubility of some classes of finite groups[J];Science in China(Series A:Mathematics);2009年02期
5 ;Finite Groups with Seminormal Sylow Subgroups[J];Acta Mathematica Sinica(English Series);2008年10期
6 贺继刚;;Efficacy of subgroup mouse bone mesenchymal stem cells on mobilizing autologous cardiac stem cells and repairing ischemic myocardial tissue[J];China Medical Abstracts(Internal Medicine);2013年02期
7 M.M.Al-Mosa Al-Shomrani;M.Ramadan;A.A.Heliel;;FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE WEAKLY H-SUBGROUPS[J];Acta Mathematica Scientia;2012年06期
8 ;Some Properties of Divisible and Pure Fuzzy Subgroups[J];模糊系统与数学;1992年01期
9 ;On Generalized PST-groups[J];Communications in Mathematical Research;2011年04期
10 Xiaojian MA;Yuemei MAO;;On Φ-τ-Supplement Subgroups of Finite Groups[J];Journal of Mathematical Research with Applications;2017年03期
11 AN LiJian;LI LiLi;QU HaiPeng;ZHANG QinHai;;Finite p-groups with a minimal non-abelian subgroup of index p(Ⅱ)[J];Science China(Mathematics);2014年04期
12 ;On SS-quasinormal subgroups and the structure of finite groups[J];Science China(Mathematics);2011年03期
13 ;On s-Quasinormal and c-Normal Subgroups of a Finite Group[J];Acta Mathematica Sinica(English Series);2008年04期
14 A.N.SKIBA;;Criteria of Existence of Hall Subgroups in Non-soluble Finite Groups[J];Acta Mathematica Sinica(English Series);2010年02期
15 王萼芳;EQUICENTRALIZER SUBGROUPS OF SYMMETRIC AND ALTER NATING GROUPS[J];A Monthly Journal of Science;1984年08期
16 BALLESTER-BOLINCHES Adolfo;COSME-LL′OPEZ Enric;KAMORNIKOV Sergey Fedorovich;;On subgroup functors of finite soluble groups[J];Science China(Mathematics);2017年03期
17 GUO WenBin;SKIBA Alexander N.;YANG NanYing;;A generalized CAP-subgroup of a finite group[J];Science China(Mathematics);2015年10期
18 郝成功;靳竹萱;;FINITE p-GROUPS WHICH CONTAIN A SELF-CENTRALIZING CYCLIC NORMAL SUBGROUP[J];Acta Mathematica Scientia;2013年01期
19 Yufeng LIU;Xiaolong YU;Lijun HUO;;On ζ_s -Quasinormality of 2-Maximal Subgroups[J];数学研究及应用;2013年04期
20 Libo ZHAO;Lü GONG;;Finite p-Groups with Large or Small Normal Closures of Non-Normal Cyclic Subgroups[J];Journal of Mathematical Research with Applications;2017年02期
中国重要会议论文全文数据库 前10条
1 ;Homomorphism and Isomorphism of Fuzzy Group[A];第六届中国不确定系统年会论文集[C];2008年
2 Wu Wen;Li Ping;Zuo Ran;Zeng Qingbo;Wu Desheng;Xie Ni;Long Dingxin;Yuan Jianhui;;The correlation between polymorphism of DNA methyltransferase 3B-149C/T and cancer risk:a meta-analysis[A];中国毒理学会第七次全国会员代表大会暨中国毒理学会第六次中青年学者科技论坛论文摘要[C];2018年
3 Lin Shi;Qing Cui;Dongmei Xie;;Group tracking control of second-order multi-agent systems[A];第36届中国控制会议论文集(A)[C];2017年
4 Chen CHEN;Lin WANG;Haoxin SHEN;Huwei SONG;Yaling ZHAO;Guanjun ZHANG;Wenzhi LI;Ma LI;Zhimin GENG;;Who Benefits from R0 Resection? A Single-center Analysis of Patients with Stage IV Gallbladder Cancer[A];第十九届中国科协年会——分10微创外科高峰论坛论文集[C];2017年
5 Shuo Dai;Yong Zhang;Limin Jia;Yong Qin;;A Subgroup Discovery Algorithm Based on Genetic Fuzzy Systems[A];2015年中国智能自动化学术会议论文集(第一分册)[C];2015年
6 ;Reducing Discrete Logarithm Problem of Conic Curve Over GF(2~n) to Discrete Logarithm Problem of Finite Field[A];2007通信理论与技术新发展——第十二届全国青年通信学术会议论文集(上册)[C];2007年
7 Zhang Luo;Song Xing;Shao Yingjie;Wu Changping;Jiang Jingting;;Prognostic value of Midkine expression in patients with solid tumors:A systematic review and meta-analysis[A];第十二届全国免疫学学术大会摘要汇编[C];2017年
8 Barsalote Eda Marie;Munawar Maria;Tian Zhongling;Cai Ruihang;Li Xiaolin;Qu Nan;郑经武;;Characterization and diagnostics of stubby root nematode Trichodorus cedarus Yokoo,1964(Dorylaimida:Trichodoridae)from Zhejiang Province,China[A];中国植物病理学会2017年学术年会论文集[C];2017年
9 黄春苹;;The spectral analysis of two Z sources[A];中国天文学会2011年学术年会手册[C];2011年
10 Fei Jiang;Fanglan Hong;Xiaobing Shen;;A Meta-analysis About CircRNAAs the Biomarker of Gastric Cancer[A];中国毒理学会第七次全国会员代表大会暨中国毒理学会第六次中青年学者科技论坛论文摘要[C];2018年
中国博士学位论文全文数据库 前4条
1 Farai.A.Abdunabi;[D];华中师范大学;2015年
2 Venus Amjid;[D];中国科学技术大学;2019年
3 Abid Mahboob;[D];中国科学技术大学;2015年
4 沙诺(Yeshanew Zeirhun Ayele);分次代数上的融合群[D];华中师范大学;2014年
中国硕士学位论文全文数据库 前1条
1 苛塔 巴拉克;幂零群和可解群的一些研究[D];安徽师范大学;2004年
 快捷付款方式  订购知网充值卡  订购热线  帮助中心
  • 400-819-9993
  • 010-62982499
  • 010-62783978