共查询到20条相似文献,搜索用时 609 毫秒
1.
HX群是由一个群向其幂集上提升的群结构.文[1]将HX群推广到一类特殊的格-原子格L上,称之为AHX群.本文研究了一类特殊的AHX群-拟L商群的同态与同构,获得与拟商群相类似的结果. 相似文献
2.
M. J. Curran 《代数通讯》2013,41(1):389-397
The article considers when the direct product of two finite groups has an Abelian automorphism group. 相似文献
3.
Jan Jakubik 《Czechoslovak Mathematical Journal》2001,51(1):127-138
The notion of the half linearly ordered group (and, more generally, of the half lattice ordered group) was introduced by Giraudet and Lucas [2]. In the present paper we define the lexicographic product of half linearly ordered groups. This definition includes as a particular case the lexicographic product of linearly ordered groups. We investigate the problem of the existence of isomorphic refinements of two lexicographic product decompositions of a half linearly ordered group. The analogous problem for linearly ordered groups was dealt with by Maltsev [5]; his result was generalized by Fuchs [1] and the author [3]. The isomorphic refinements of small direct product decompositions of half lattice ordered groups were studied in [4]. 相似文献
4.
A finite group G is called rational if all its irreducible complex characters are rational valued. In this paper, we show that if G is a direct product of finitely many rational Frobenius groups then every rationally represented character of G is a generalized permutation character. Also we show that the same assertion holds when G is a solvable rational group with a Sylow 2-subgroup isomorphic to the dihedral group of order 8 and an abelian normal Sylow 3-subgroup. 相似文献
5.
文章先利用自同构映射保有限并的性质研究了一般正交模格的次直积的自同构群与自同构群的次直积的关系,再用块置换的方法研究了MOk的自同构群的生成元集,由此得到自由正交模格FMOk(n)的自同构群的直积分解式,从而完全解决了FMOk(n)的自同构群的结构问题. 相似文献
6.
G. Hughes 《Designs, Codes and Cryptography》2001,24(1):5-14
Using ideas from the cohomology of finite groups, an isomorphism is established between a group ring and the direct sum of twisted group rings. This gives a decomposition of a group ring code into twisted group ring codes. In the abelian case the twisted group ring codes are (multi-dimensional) constacyclic codes. We use the decomposition to prove that, with respect to the Euclidean inner product, there are no self-dual group ring codes when the group is the direct product of a 2-group and a group of odd order, and the ring is a field of odd characteristic or a certain modular ring. In particular, there are no self-dual abelian codes over the rings indicated. Extensions of these results to non-Euclidean inner products are briefly discussed. 相似文献
7.
Mark Pedigo 《代数通讯》2013,41(11):4462-4475
In their article, “On the derived subgroup of the free nilpotent groups of finite rank” R. D. Blyth, P. Moravec, and R. F. Morse describe the structure of the derived subgroup of a free nilpotent group of finite rank n as a direct product of a nonabelian group and a free abelian group, each with a minimal generating set of cardinality that is a given function of n. They apply this result to computing the nonabelian tensor squares of the free nilpotent groups of finite rank. We generalize their main result to investigate the structure of the other terms of the lower central series of a free nilpotent group of finite rank, each again described as a direct product of a nonabelian group and a free abelian group. In order to compute the ranks of the free abelian components and the size of minimal generating sets for the nonabelian components we introduce what we call weight partitions. 相似文献
8.
On the Affine Completeness of Lattice Ordered Groups 总被引:2,自引:2,他引:0
Ján Jakubík 《Czechoslovak Mathematical Journal》2004,54(2):423-429
In the paper it is proved that a nontrivial direct product of lattice ordered groups is never affine complete. 相似文献
9.
10.
Jan Jakubik 《Czechoslovak Mathematical Journal》2001,51(3):661-671
The distinguished completion E(G) of a lattice ordered group G was investigated by Ball [1], [2], [3]. An analogous notion for MV-algebras was dealt with by the author [7]. In the present paper we prove that if a lattice ordered group G is a direct product of lattice ordered groups G
i
(i I), then E(G) is a direct product of the lattice ordered groups E(G
i). From this we obtain a generalization of a result of Ball [3]. 相似文献
11.
在这篇注记中,通过研究两个有限群直积的整群环的正规化挠单位的偏增广,证明了在某些条件下这些正规化挠单位与该群中的元素在有理群代数中共轭. 相似文献
12.
13.
V. I. Senashov 《Mathematical Notes》1997,62(4):480-487
The class of generalized Chernikov groups is characterized, i.e., the class of periodic locally solvable groups with the primary
ascending chain condition. The name of the class is related to the fact that the structure of such groups is close to that
of Chernikov groups. Namely, a Chernikov group is defined as a finite extension of a direct product of finitely many quasi-cyclic
groups, and a generalized Chernikov group is a layer-finite extension of a direct productA of quasi-cyclicp-groups with finitely many factors for each primep such that each of its elements does not commute elementwise with only finitely many Sylow subgroups ofA. A theorem that characterizes the generalized Chernikov groups in the class of groups with involution is proved.
Translated fromMatematicheskie Zametki, Vol. 62, No 4, pp. 577–587, October, 1997.
Translated by A. I. Shtern 相似文献
14.
15.
Ihechukwu Chinyere 《代数通讯》2018,46(3):1138-1154
In this paper and a sequel, we study a group which is the quotient of a free product of groups by the normal closure of a single word that is contained in a subgroup which has the form of a free product of two cyclic groups. We use known properties of generalized triangle groups, together with detailed analysis of pictures and of words in free monoids, to prove a number of results such as a Freiheitssatz and the existence of Mayer-Vietoris sequences for such groups under suitable hypotheses. The results generalize those in an earlier article of the second author and Shwartz. 相似文献
16.
在不改变对角方阵各行、各列、主对角线、次对角线的元素之集的条件下,其变换群是n次对称群S_n的直积S_n×S_n的子群,因对角拉丁方、对角拉丁方正交侣、幻方、高次幻方、加乘幻方均属此类方阵,本文对构作这类对象及研究它们的计数有重要意义. 相似文献
17.
Ignacio Bajo 《Geometriae Dedicata》1997,66(3):281-291
Lie groups with bi-invariant semi-Riemannian metrics are considered. We study the decomposition of the algebra of prederivations of a direct sum of Lie algebras and derive some results on the isotropy group of a bi-invariant product Lie group. We also give necessary and sufficient conditions to ensure that all isometries of a complex Lie group, endowed with a bi-invariant Norden metric, are holomorphic. 相似文献
18.
本文利用Luthar-Passi方法,研究了五次交错群A_5与六阶二面体群D_6直积的整群环的挠单位,得到了该群的Zassenhaus猜想成立. 相似文献
19.
一类环上HX环的结构 总被引:11,自引:2,他引:9
自李洪兴1991年提出了HX环以来,人们一直有这么一个问题没解决,就是是否存在非平凡的HX环的例子?但至今既没找到非平凡的HX环,也没有证明任一环R仅存在平凡的HX环。针对这个问题,本文提出并证明了一类环仅有平凡HX环,还给出了一系列的结构定理。这样,既为证明任一环R仅有平凡的HX环的猜想有新的启示,也为人们指明无须在这一类环上寻找非平凡HX环。 相似文献
20.
Mariusz Grech 《Journal of Graph Theory》2009,62(1):26-36
In this article we study the product action of the direct product of automorphism groups of graphs. We generalize the results of Watkins [J. Combin Theory 11 (1971), 95–104], Nowitz and Watkins [Monatsh. Math. 76 (1972), 168–171] and W. Imrich [Israel J. Math. 11 (1972), 258–264], and we show that except for an infinite family of groups Sn × Sn, n≥2 and three other groups D4 × S2, D4 × D4 and S4 × S2 × S2, the direct product of automorphism groups of two graphs is itself the automorphism group of a graph. © 2009 Wiley Periodicals, Inc. J Graph Theory 62: 26–36, 2009 相似文献