共查询到20条相似文献,搜索用时 0 毫秒
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Dimitrios Ballas 《代数通讯》2017,45(2):481-492
In this paper, we show that the injective dimension of all projective modules over a countable ring is bounded by the self-injective dimension of the ring. We also examine the extent to which the flat length of all injective modules is bounded by the flat length of an injective cogenerator. To that end, we study the relation between these finiteness conditions on the ring and certain properties of the (strict) Mittag–Le?er modules. We also examine the relation between the self-injective dimension of the integral group ring of a group and Ikenaga’s generalized (co-)homological dimension. 相似文献
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Imke Toborg 《Aequationes Mathematicae》2016,90(4):699-704
We analyse Tabor groups where every element has finite order and we characterise finite Tabor groups. 相似文献
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V. I. Senashov 《Ukrainian Mathematical Journal》1999,51(4):525-537
We prove a theorem that describes almost layer-finite groups in the class of conjugatively biprimitive-finite groups. Computer Center of the Siberian Division of the Russian Academy of Sciences, Krasnoyarsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 472–485, April, 1999. 相似文献
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E. I. Timoshenko 《Algebra and Logic》1973,12(2):132-137
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Lucio S. Cirio Alessandro D'Andrea Claudia Pinzari Stefano Rossi 《Journal of Functional Analysis》2014
We introduce the notion of identity component of a compact quantum group and that of total disconnectedness. As a drawback of the generalized Burnside problem, we note that totally disconnected compact matrix quantum groups may fail to be profinite. We consider the problem of constructing the identity component by introducing canonical approximating transfinite sequences of subgroups. These sequences have lengths ≤1 in the classical case but can be countably infinite for duals of discrete groups. We give examples of free product quantum groups where the identity component is not normal and the associated sequence has length 1. 相似文献
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We consider the following two finiteness conditions on normalizers and centralizers in a group G: (i) |NG(H) : H| < ∞ for every H ? G, and (ii) |CG(x):?x?|<∞ for every ?x??G. We show that (i) and (ii) are equivalent in the classes of locally finite groups and locally nilpotent groups. In both cases, the groups satisfying these conditions are a special kind of cyclic extensions of Dedekind groups. We also study a variation of (i) and (ii), where the requirement of finiteness is replaced with a bound. In this setting, we extend our analysis to the classes of periodic locally graded groups and non-periodic groups. While the two conditions are still equivalent in the former case, in the latter the condition about normalizers is stronger than that about centralizers. 相似文献
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S. V. Lenyuk 《Algebra and Logic》1996,35(5):310-315
Let ℳ be a quasivariety of torsion-free groups satisfying the identity (∀x)(∀y)(x
2,y
2)=1. It is proved that the lattice of quasivarieties contained in ℳ has the power of the continuum.
Supported by RFFR grant No. 93-011-1524.
Translated fromAlgebra i Logika, Vol. 35, No. 5, pp. 552–561, September–October, 1996. 相似文献
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Let M be a finitely generated metabelian group explicitly presented in a variety of all metabelian groups. An algorithm is constructed which, for every endomorphism φ ∈ End(M) identical modulo an Abelian normal subgroup N containing the derived subgroup M′ and for any pair of elements u, v ∈ M, decides if an equation of the form (xφ)u = vx has a solution in M. Thus, it is shown that the title problem under the assumptions made is algorithmically decidable. Moreover, the twisted
conjugacy problem in any polycyclic metabelian group M is decidable for an arbitrary endomorphism φ ∈ End(M).
Supported by RFBR (project No. 07-01-00392). (V. A. Roman’kov)
Translated from Algebra i Logika, Vol. 48, No. 2, pp. 157–173, March–April, 2009. 相似文献
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David J. Rusin 《Journal of Pure and Applied Algebra》1980,18(3):283-291
A knowledge of the simple representation theory of finite abelian groups is useful for understanding the representations of solvable groups, since these provide the one-dimensional representations. The representation theory of metabelian groups (those G with abelian commutator subgroup G′) would seem to be a natural next level.In this paper we shall show that these representations, too, may be simply described in several ways: they are induced from linear representations of some explicity defined subgroups; their degrees may be calculated from a knowledge of the subgroups of G; these degrees depend only on the kernel of the representation (in fact, only on the intersection of this kernel with G′). As an application of these results, we can calculate for metabelian groups a certain measure of group-commutativity studied in an earlier paper [4]. 相似文献
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We look at properties of partially commutative metabelian groups and of their universal theories. In particular, it is shown
that two partially commutative metabelian groups defined by cycles are universally equivalent if and only if the cycles are
isomorphic. 相似文献