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1.
I. E. Grinshpon 《Journal of Mathematical Sciences》2008,154(3):284-289
Two groups are said to be almost holomorphically isomorphic if each of them is isomorphic to a normal subgroup of the holomorph
of the other group. In this paper, we study normal subgroups of holomorphs of Abelian groups and highlight some torsion-free
groups for which almost holomorphic isomorphism implies isomorphism. In addition, we consider the problem of determinateness
of a group by its holomorph.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 3, pp. 9–16, 2007. 相似文献
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《Expositiones Mathematicae》2021,39(3):354-368
Since solitary subgroups of (infinite) Abelian groups are precisely the strictly invariant subgroups which are co-Hopfian (as groups), and strictly invariant subgroups turn out to be strongly invariant for large classes of Abelian groups we determine the solitary subgroups for these classes of groups. 相似文献
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Witold Jarczyk 《Aequationes Mathematicae》2010,80(1-2):141-154
The notion of almost convexity is studied and an extension of Kuczma’s theorem, originally proved in finite-dimensional spaces, is presented. The phrase “almost” is meant in the sense of abstract σ-ideals. The main result also generalizes the theorem proved in Jarczyk and Laczkovich (Math Inequal Appl 13:217–225, 2009). 相似文献
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LetX be a torsion-free abelian group. We study the class of all completely decomposable subgroups ofX which are maximal with respect to inclusion. These groups are called tight subgroups ofX and we state sufficient conditions on a subgroup to be tight. In particular we consider tight subgroups of bounded completely
decomposable groups. For those we show that every regulating subgroup is tight and we characterize the tight subgroups of
finite index in almost completely decomposable groups.
The second author was supported by a MINERVA fellowship. 相似文献
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A subgroup \(H\) of an Abelian group \(G\) is called fully inert if \((\phi H + H)/H\) is finite for every \(\phi \in \mathrm{End}(G)\) . Fully inert subgroups of free Abelian groups are characterized. It is proved that \(H\) is fully inert in the free group \(G\) if and only if it is commensurable with \(n G\) for some \(n \ge 0\) , that is, \((H + nG)/H\) and \((H + nG)/nG\) are both finite. From this fact we derive a more structural characterization of fully inert subgroups \(H\) of free groups \(G\) , in terms of the Ulm–Kaplansky invariants of \(G/H\) and the Hill–Megibben invariants of the exact sequence \(0 \rightarrow H \rightarrow G \rightarrow G/H \rightarrow 0\) . 相似文献
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Mathematical Notes - It is shown that every homogeneous separable torsion-free group is strongly invariant simple (i.e., has no nontrivial strongly invariant subgroups) and, for a completely... 相似文献
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A. R. Chekhlov 《Journal of Mathematical Sciences》2010,164(1):143-147
The properties of projective invariant subgroups are studied. The structure of these subgroups in nonreduced groups is described. The conditions under which projective invariant subgroups are fully invariant are considered. 相似文献
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P. A. Krylov 《Mathematical Notes》1976,20(6):1011-1015
We investigate the structure of indecomposable torsion-free Abelian groups all of whose p-basic subgroups are cyclic, and also the structure of the groups and rings of endomorphisms of such groups. We prove the existence of a torsion-free Abelian group of countable rank with cyclic p-basic subgroups which has no indecomposable nonzero direct summands.Translated from Matematicheskie Zametki, Vol. 20, No. 6, pp. 805–813, December, 1976. 相似文献
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We show that a finite permutation group containing a regular abelian self-normalizing subgroup is soluble. 相似文献
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S. V. Maznichenko 《Ukrainian Mathematical Journal》1998,50(5):839-841
Solvable and minimal unsolvable finite groups with cyclic Abelian subgroups are constructively described.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 5, pp. 739–741, May, 1998. 相似文献
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V. I. Zenkov 《Algebra and Logic》1996,35(3):160-163
Using the basic theorem on the classification of finite simple groups, we answer one of the questions concerning the generation
of finite groups by the class of conjugate Abelian subgroups.
Supported by RFFR grant No. 93-01-01529.
Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 288–293, May–June, 1996. 相似文献
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E. P. Vdovin 《Algebra and Logic》1999,38(2):67-83
We bring out upper bounds for the orders of Abelian subgroups in finite simple groups. (For alternating and classical groups,
these estimates are, or are nearly, exact.) Precisely, the following result, Theorem A, is proved. Let G be a non-Abelian
finite simple group and G
L2 (q), where q=pt for some prime number p. Suppose A is an Abelian subgroup of G. Then |A|3<|G|. Our proof is based on a classification of finite simple groups. As a consequence we obtain Theorem B, which states that
a non-Abelian finite simple group G can be represented as ABA, where A and B are its Abelian subgroups, iff G≌ L2(2t) for some t ≥ 2; moreover, |A|-2t+1, |B|=2t, and A is cyclic and B an elementary 2-group.
Translated fromAlgebra i Logika, Vol. 38, No. 2, pp. 131–160, March–April, 1999. 相似文献
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Measure concentration arguments are applied to get a power-type estimate for the dimension of almostl
p subspaces of isomorphs ofl
p
n
and for the length of almost-symmetric sequences under a nonlinear-type condition.
Supported by the Fund for Basic Research Administered by the Israel Academy of Sciences and Humanities. 相似文献