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 ...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.展开更多
It is a well-known fact that characters of a finite group can give important information about the structure of the group. It was also proved by the third author that a finite simple group can be uniquely determined b...It is a well-known fact that characters of a finite group can give important information about the structure of the group. It was also proved by the third author that a finite simple group can be uniquely determined by its character table. Here the authors attempt to investigate how to characterize a finite almost-simple group by using less information of its character table, and successfully characterize the automorphism groups of Mathieu groups by their orders their character tables. and at most two irreducible character degrees of展开更多
文摘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.
基金supported by the National Natural Science Foundation of China(Nos.11426182,11401324,11271301,11471266,10871032)SRF for ROCS,SEM,the Fundamental Research Funds for the Central Universities(No.SWU115052)+1 种基金the Natural Science Foundation Project of CQ CSTC(Nos.cstc2014jcyj A00010,cstc2014jcy A0148,2010BB9206)the National Science Foundation for Distinguished Young Scholars of China(No.11001226)
文摘It is a well-known fact that characters of a finite group can give important information about the structure of the group. It was also proved by the third author that a finite simple group can be uniquely determined by its character table. Here the authors attempt to investigate how to characterize a finite almost-simple group by using less information of its character table, and successfully characterize the automorphism groups of Mathieu groups by their orders their character tables. and at most two irreducible character degrees of
基金supported by NSFC(No.11671324,No.11471266)the Natural Science Foundation Project of CQ CSTC(No.cstc2015jcyjA00020)the Science and Technology Project of Chongqing Education Committee(No.KJ1600325)
