共查询到20条相似文献,搜索用时 15 毫秒
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Martino Garonzi 《代数通讯》2013,41(2):471-491
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We study solvable groups of infinite special rank all proper normal subgroups of which define quotient groups of finite special rank. 相似文献
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We continue the investigation of (solvable) groups all proper subgroups of which are hypercyclic. The monolithic case is studied completely; in the nonmonolithic case, however, one should impose certain additional conditions. We investigate groups all proper quotient groups of which possess supersolvable classes of conjugate elements. 相似文献
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Mathematical Notes - 相似文献
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《Journal of Algebra》2002,247(2):509-540
Let Fm be a free group of a finite rank m ≥ 2 and let Xi, Yj be elements in Fm. A non-empty word w(x1,…,xn) is called a C-test word in n letters for Fm if, whenever (X1,…,Xn) = w(Y1,…,Yn) ≠ 1, the two n-typles (X1,…,Xn) and (Y1,…,Yn) are conjugate in Fm. In this paper we construct, for each n ≥ 2, a C-test word vn(x1,…,xn) with the additional property that vn(X1,…,Xn) = 1 if and only if the subgroup of Fm generated by X1,…,Xn is cyclic. Making use of such words vm(x1,…,xm) and vm + 1(x1,…,xm + 1), we provide a positive solution to the following problem raised by Shpilrain: There exist two elements u1, u2 ∈ Fm such that every endomorphism ψ of Fm with non-cyclic image is completely determined by ψ(u1), ψ(u2). 相似文献
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M. Rovinsky 《Compositio Mathematica》2003,136(1):61-67
Let k be an algebraically closed field of characteristic zero, F be an algebraically closed extension of k of transcendence degree one, and G be the group of automorphisms over k of the field F. The purpose of this note is to calculate the group of continuous automorphisms of G. 相似文献
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Let w(x, y) be a word in two variables and 𝔚 the variety determined by w. In this paper we raise the following question: if for every pair of elements a, b in a group G there exists g ∈ G such that w(a g , b) = 1, under what conditions does the group G belong to 𝔚? In particular, we consider the n-Engel word w(x, y) = [x, n y]. We show that in this case the property is satisfied when the group G is metabelian. If n = 2, then we extend this result to the class of all solvable groups. 相似文献
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We classify two types of finite groups with certain normality conditions, namely SSN groups and groups with all noncyclic subgroups normal. These conditions are key ingredients in the study of the multiplicative Jordan decomposition problem for group rings. 相似文献
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Acta Mathematica Sinica, English Series - For a finite group G, the power graph $$\cal{P}(G)$$ is a simple connected graph whose vertex set is the set of elements of G and two distinct vertices x... 相似文献
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A. R. Chekhlov 《代数通讯》2013,41(12):5059-5073
We introduce two classes of abelian groups which have either only trivial fully invariant subgroups or all their nontrivial (respectively nonzero) fully invariant subgroups are isomorphic, called IFI-groups and strongly IFI-groups, such that every strongly IFI-group is an IFI-group, respectively. Moreover, these classes coincide when the groups are torsion-free, but are different when the groups are torsion as well as, surprisingly, mixed groups cannot be IFI-groups. We also study their important properties as our results somewhat contrast with those from [13] and [14]. 相似文献
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A. Doostabadi 《代数通讯》2013,41(10):4305-4319
We study the connectivity of proper power graphs of some family of finite groups including nilpotent groups, groups with a nontrivial partition, and symmetric and alternating groups. Also, for such a group, the corresponding proper power graph has diameter at most 26 whenever it is connected. 相似文献
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§0 引言 A=(α_(ij))是n阶广义Cantan矩阵,即A满足:ⅰ)α_(ii)=2,i=1,…n。ⅱ)当i≠j时,α_(ij)是非正整数。ⅲ) a_(ij)=0 α_(ji)=0。 h是复数域C上2n-l维向量空间,h是h的对偶空间。Π={α_1,…α_n},Π分别是h与h中线性无关子集,满足 相似文献
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Mathematical Notes - It is proved that, in any finite group $$G$$ with nilpotent subgroups $$A$$ and $$B$$ and the condition $$A\cap B^g\unlhd\langle A,B^g\rangle$$ for any $$g$$ in $$G$$ ,... 相似文献
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For an arbitrary variety
of groups and an arbitrary class
of groups that is closed on quotient groups, we prove that a quotient group G/N of the group G possesses an invariant system with
- and
-factors (respectively, is a residually
-group) if G possesses an invariant system with
- and
-factors (respectively, is a residually
-group) and N
(respectively, N is a maximal invariant
-subgroup of the group G). 相似文献
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L. M. EZQUERRO X. SOLER-ESCRIVA 《数学学报(英文版)》2007,23(11):2069-2078
In this paper, we prove the following result. Let ξ be a saturated formation and ∑ a Hall system of a soluble group G. Let X be a w-solid set of maximal subgroups of G such that ∑ reduces into each element of X. Consider in G the following three subgroups: the ξ-normalizer D of G associated with ∑; the X-prefrattini subgroup W = W(G, X) of G; and a hypercentrally embedded subgroup T of G. Then the lattice ζ(T, W, D) generated by T, D and W is a distributive lattice of pairwise permutable subgroups of G with the cover and avoidance property.
This result remains true for the lattice ,ζ(V, W, D), where V is a subgroup of G whose Sylow subgroups are also Sylow subgroups of hypercentrally embedded subgroups of G such that ∑ reduces into V. 相似文献
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We extend the Dikranjan-Uspenskij notions of c-compact and h-complete topological group to the morphism level, study the stability properties of the newly defined types of maps, such as closure under direct products, and compare them with their counterparts in topology. We assume Hausdorffness only when our proofs require us to do so, which leads to new results and the affirmation of some facts that were known in a Hausdorff context. 相似文献
18.
We consider three infinite families of cyclic presentations of groups, depending on a finite set of integers and having the same polynomial. Then we prove that the corresponding groups with the same parameters are isomorphic, and that the groups are almost all infinite. Finally, we completely compute the maximal Abelian quotients of such groups, and show that their HNN extensions are high-dimensional knot groups. Our results contain as particular cases the main theorems obtained in two nice articles: Johnson et al. (1999) and Havas et al. (2001). 相似文献
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