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本文给出了两个非平凡可数格序群的l-自由积在有理数集Q上的高o-可迁忠实表示。证明了格序群的l-自由积的向量格复盖与格序群的向量格复盖的l-自由积之间的同构关系;格序群与格序群的反向系统的l-自由积的反向极限与反向极限的自由积之间的同构关系。作为应用,本文给出了两个非平凡可数格序群的l-自由积的复盖在Q上的高o-可迁忠实表示和下有向偏序集上的非平凡可数格序群的反向系统的反向极限在Q上的高o-可迁忠 相似文献
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左剩余格序广群上的矩阵方程 总被引:1,自引:1,他引:0
研究左剩余格序广群L上矩阵方程AX=B的解集以及所有n阶矩阵的集合Mn(L),将文献[3]中的一切结果推广到左剩余格序广群上,而且证明了若L是左剩余格序广群,则Mn(L)也组成左剩余格序广群。此外,还指出了文献[1]中主要结论的错误。 相似文献
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本文利用非交换格序群的一个例,证明了交换格序群一些命题中交换性条件的必要性。例令G是一个群有三个无穷阶、线性无关的生成元a,b,c;并且定义关系a+b=b+a,a+c—c+b,b+c—c+a;G~+包含ma+m'b+nc当且仅当n>0或n—0而m≥O,m'≥0。 相似文献
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引入弱奇异元及弱奇异l-群的概念,通过建立弱奇异元及弱奇异l-群的刻划,研究了一般弱奇异l-群的性质及相关的结构,部分地改进了有关奇异l-群已有的结果. 相似文献
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本文给出了格序群的扭类是准素扭类的一个充分必要条件,证明了任一非零扭类至少包含一个极小扭类,从而将文〔1〕和〔2〕中在有限制条件情况下的有关结论推广到无任何限制条件的情形。本文还给出了一个扭类是极扭类的几个充分必要条件,并得到了格序群的极扭类、准素扭类和极小扭类之间的关系。 相似文献
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Summary A subgroup H of a group G is said to be π-quasinormal in G if it permutes with every Sylow subgroup of G, and H is said to be π-quasinormally embedded in G if for each prime dividing the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some π-quasinormal subgroups of G. We characterize p-nilpotentcy of finite groups with the assumption that some maximal subgroups, 2-maximal subgroups, minimal subgroups and 2-minimal subgroups are π-quasinormally embedded, respectively. 相似文献
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The structure of finite solvable groups in which any Sylow subgroup is the product of two cyclic subgroups is studied. In particular, it is proved that the nilpotent length of such a group is no greater than 4. It is also proved that the nilpotent length of a finite solvable group in which the index of any maximal subgroup is either a prime or the square of a prime or the cube of a prime does not exceed 5. 相似文献
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We study the influence of τ-primitive subgroups on the structure of finite groups. As applications, we give the structure of the finite groups whose every subgroup is an intersection of subgroups of prime power index and the structure of finite groups whose every subnormal subgroup is an intersection of subnormal subgroups of prime power index. 相似文献
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Let d be the smallest generator number of a finite p-group P, and let be a set of maximal subgroups of P such that . In this paper, the structure of a finite group G under some assumptions on the S-quasinormally embedded or SS-quasinormal subgroups in , for each prime p, and Sylow p-subgroups P of G is studied. 相似文献
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能表示成四个真子群并的有限群 总被引:1,自引:1,他引:0
本文研究了子群覆盖问题.利用计算子群阶的方法,给出了能表示成p+1或p+2个真子群并的有限群G的结构,这里p是群G阶的最小素因子,从而推广了文献[1]中的结果. 相似文献
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Congruence subgroups of Hecke groups 总被引:1,自引:0,他引:1
Hecke groups are an important tool in subgroups of Hecke groups play an important rule investigating functional equations, and congruence in research of the solutions of the Dirichlet series. When q, m are two primes, congruence subgroups and the principal congruence subgroups of level m of the Hecke group H(√q) have been investigated in many papers. In this paper, we generalize these results to the case where q is a positive integer with q ≥ 5, √q ¢ Z and m is a power of an odd prime. 相似文献
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《代数通讯》2013,41(5):2019-2027
Abstract A subgroup of a group G is said to be S-quasinormal in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be S-quasinormally embedded in G if every Sylow subgroup of H is a Sylow subgroup of some S-quasinormal subgroup of G. In this paper we examine the structure of a finite group G under the assumption that certain abelian subgroups of prime power order are S-quasinormally embedded in G. Our results improve and extend recent results of Ramadan [Ramadan, M. (2001). The influence of S-quasinormality of some subgroups of prime power order on the structure of finite groups. Arch. Math. 77:143–148]. 相似文献
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Nihal YILMAZ OZGUR 《数学学报(英文版)》2006,22(2):383-392
Using the notion of quadratic reciprocity, we discuss the principal congruence subgroups of the Hecke groups H(√q),q 〉 5 prime number. 相似文献