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On Some Embedment of Groups into wreath products

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Advances in Pure Mathematics 2021年第2期11卷 109-120页

作者： Enoch Suleiman Muhammed Salihu Audu Department of Mathematics Federal University Gashua Yobe State Nigeria Department of Mathematics University of Jos Jos Nigeria

In this paper, we showed how groups are embedded into wreath products, we gave a simpler proof of the theorem by Audu (1991) (see [1]), also proved that a group can be embedded into the wreath product of a factor group by a normal subgroup and also proved that a factor group can be embedded inside a wreath product and the wreath product of a factor group by a factor group can be embedded into a group. We further showed that when the abstract group in the Universal Embedding Theorem is a p-group, cyclic and simple, the embedding becomes an isomorphism. Examples were given to justify the results.

关键词： wreath product Direct product Homomorphism Embedding p-Group Cyclic Simple

Finite Groups in Which Sylow Normalizers Admit Supplements

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Acta Mathematica Sinica,English Series 2007年第3期23卷 417-422页

作者： Tian Ze LI School of Mathematical Sciences,Peking University,Beijing 100871,P.R.China School of Mathematical Sciences Peking University Beijing 100871 P. R. China

For a group G and a subgroup M of G,we say that a subgroup A of G is a supplement toM in G,if G=*** prove that a finite group in which every Sylow normalizer admits a nilpotentsupplement is *** particular we confirm a... 详细信息

关键词： Sylow normalizer Supplement wreath product

wreath Hurwitz numbers,colored cut-and-join equations,and 2-Toda hierarchy

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Science China Mathematics 2012年第8期55卷 1627-1646页

作者： ZHANG HanXiong ZHOU Jian Department of Mathematical Sciences Tsinghua University Beijing 100084 China Email: zhanghanxiong @163. corn jzhou~math tsinghua edu. cn

Let G be arbitrary finite group,define H G· (t;p +,p) to be the generating function of G-wreath double Hurwitz *** prove that H G· (t;p +,p) satisfies a differential equation called the colored cutand-join ***,H G·(t;p +,p) is a product of several copies of tau functions of the 2-Toda hierarchy,in independent *** generalize the corresponding results for ordinary Hurwitz numbers.

关键词： Hurwitz number wreath product cut-and-join equation integrable hierarchy

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One Class of the Least Congruences on Completely Regular Semigroups

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Journal of Donghua University(English Edition) 2021年第3期38卷 278-282页

作者： ZHANG Jiangang SHEN Ran Department of Mathematics Shanghai Normal University Shanghai 200234 China College of Science Donghua University Shanghai 201620 China

Congruence is a very important aspect in the study of the semigroup *** general,the Kernel-trace characterizations,Green's relations and subvarieties are main tools in the consideration of congruences on completely regular *** this paper,we give one class of congruences on completely regular semigroups with the representation of wreath product of translational hulls on completely simple *** this new way,the least Clifford semigroup congruences on completely regular semigroups are generalized.

关键词： completely regular semigroup Clifford congruence translational hull wreath product orthogroup

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GF(2)-modules for Sz (q) wrC_t

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Chinese Quarterly Journal of Mathematics 1997年第4期12卷 87-90,页

作者：王秀琴熊胜利 Department of

In this note the authors investigates the property of the GF(2)-modules for the wreath products Sz(q)wrCt,and establish some sufficient condition for a Sz(q)wrCt, GF(2)-module to be natural.

关键词： wreath product natural module chief factor irreducible module

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On the Structure of Some Groups Containing L2 （11） wrM12

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Journal of Mathematics and System Science 2013年第1期3卷 1-4页

作者： Basmah H. Shafee Department of Mathematics Faculty of Applied Sciences Umm Al-Qura University Makkah 21421 Saudi Arabia

In this paper, we generate the wreath product L2 （1 1） wrM12 using only two permutations. Also, we show the structure of some groups containing the wreath product L2（1 1）wrM12. The structure of the groups founded is determined in terms of wreath product （L2 （11）wrM12）wrCt. Some related cases are also included. Also, we will show that S132K＋1 and A132K＋l can be generated using the wreath product （L2 （1 1）wrM12） wr Ck and a transposition in S132K＋1 and an element of order 3 in A132K＋l. We will also show that S132K＋1 and A132K＋1 can be generated using the wreath product L2 （1 1） wrMl2 and an element of order k ＋ 1.

关键词： wreath product Mathieu group linear group.