共查询到20条相似文献,搜索用时 15 毫秒
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Jonathan A. Hillman 《Commentarii Mathematici Helvetici》1988,63(1):664-671
We show that a torsion free abelian normal subgroup of rank two of a two-knot group which is contained in the commutator subgroup
must be free abelian, the centralizer of the abelian subgroup is not contained in the commutator subgroup, and neither of
the latter two groups is finitely generated. Furthermore, we characterize algebraically the groups of 2-knots which are cyclic
branched covers of twist spun torus knots. 相似文献
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Philippe Graftieaux 《Inventiones Mathematicae》2001,145(1):1-17
In this paper, we generalize the result of [12] in the following sense. Let A be an abelian variety over a number field k, let ? be the Néron model of A over the ring of integers O
k
of k. Completing ? along its zero section defines a formal group over O
k
. We prove that any formal subgroup of the generic fiber of whose closure in is smooth over an open subset of Spec O
k
arises in fact from an abelian subvariety of A. The proof is of a transcendental nature and uses the Arakelovian formalism introduced by Bost [3].
Oblatum 2-V-2000 & 28-XI-2000?Published online: 5 March 2001 相似文献
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Joshua Buckner 《Journal of Pure and Applied Algebra》2007,211(2):392-399
Let {0}≠K be a subgroup of the abelian group G. In [J. Buckner, M. Dugas, Co-local subgroups of abelian groups, in: Abelian Groups, Rings, Modules, and Homological Algebra, in: Lect. Notes Pure and Appl. Math., vol. 249, Chapman & Hall/CRC, Boca Raton, FL, 2006, pp. 29-37], K was called a co-local (cl) subgroup of G if is naturally isomorphic to . We generalize this notion to the quasi-category of abelian groups and call the subgroup K≠{0} of G a quasi-co-local (qcl) subgroup of G if is naturally isomorphic to . We show that qcl subgroups behave quite differently from cl subgroups. For example, while cl subgroups K are pure in G, i.e. G/K is torsion-free if G is torsion-free, any reduced torsion group T can be the torsion subgroup t(G/K) of G/K where G is torsion-free and K is a qcl subgroup of G. 相似文献
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We prove that every countable subgroup of a compact metrizable abelian group has a characterizing set. As an application, we answer several questions on maximally almost periodic (MAP) groups and give a characterization of the class of (necessarily MAP) abelian topological groups whose Bohr topology has countable pseudocharacter. 相似文献
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Czechoslovak Mathematical Journal - We say that a subgroup H is isolated in a group G if for every x ∈ G we have either x ∈ H or 〈x〉 ∩ H = 1. We describe the set of... 相似文献
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Manfred Dugas 《Journal of Pure and Applied Algebra》2007,208(1):117-126
In [J. Buckner, M. Dugas, Co-local subgroups of abelian groups, in: Abelian Groups, Rings, Modules, and Homological Algebra, in: Lect. Notes Pure and Applied Math., vol. 249, Taylor and Francis/CRC Press, pp. 25-33] the notion of a co-local subgroup of an abelian group was introduced. A subgroup K of A is called co-local if the natural map is an isomorphism. At the center of attention in [J. Buckner, M. Dugas, Co-local subgroups of abelian groups, in: Abelian Groups, Rings, Modules, and Homological Algebra, in: Lect. Notes Pure and Applied Math., vol. 249, Taylor and Francis/CRC Press, pp. 25-33] were co-local subgroups of torsion-free abelian groups. In the present paper we shift our attention to co-local subgroups K of mixed, non-splitting abelian groups A with torsion subgroup t(A). We will show that any co-local subgroup K is a pure, cotorsion-free subgroup and if D/t(A) is the divisible part of A/t(A)=D/t(A)⊕H/t(A), then K∩D=0, and one may assume that K⊆H. We will construct examples to show that K need not be a co-local subgroup of H. Moreover, we will investigate connections between co-local subgroups of A and A/t(A). 相似文献
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Peter V. Danchev 《Czechoslovak Mathematical Journal》2002,52(1):129-140
Suppose
is a commutative ring with identity of prime characteristic
and
is an arbitrary abelian
-group. In the present paper, a basic subgroup and a lower basic subgroup of the
-component
and of the factor-group
of the unit group
in the modular group algebra
are established, in the case when
is weakly perfect. Moreover, a lower basic subgroup and a basic subgroup of the normed
-component
and of the quotient group
are given when
is perfect and
is arbitrary whose
is
-divisible. These results extend and generalize a result due to Nachev (1996) published in Houston J. Math., when the ring
is perfect and
is
-primary. Some other applications in this direction are also obtained for the direct factor problem and for a kind of an arbitrary basic subgroup. 相似文献
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Takashi Okuyama 《代数通讯》2013,41(1):121-139
We determine the structure of a p-pure[pure] hull of a p-purifiable [purifiable] subgroup of an arbitrary abelian group. Moreover, we prove that a subgroup A of an abelian group G is purifiable in G if and only if A is p-purifiable in G for every prime p. Using these results, we characterize the groups G for which all subgroups are purifiable in G. Furthermore, we establish several properties of purifiable subgroups. 相似文献
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Peter Danchev 《Czechoslovak Mathematical Journal》2007,57(1):173-182
Suppose F is a perfect field of char F = p ≠ 0 and G is an arbitrary abelian multiplicative group with a p-basic subgroup B and p-component G
p
. Let FG be the group algebra with normed group of all units V(FG) and its Sylow p-subgroup S(FG), and let I
p
(FG; B) be the nilradical of the relative augmentation ideal I(FG; B) of FG with respect to B.
The main results that motivate this article are that 1 + I
p
(FG; B) is basic in S(FG), and B(1 + I
p
(FG; B)) is p-basic in V(FG) provided G is p-mixed. These achievements extend in some way a result of N. Nachev (1996) in Houston J. Math. when G is p-primary. Thus the problem of obtaining a (p-)basic subgroup in FG is completely resolved provided that the field F is perfect.
Moreover, it is shown that G
p
(1 + I
p
(FG; B))/G
p
is basic in S(FG)/G
p
, and G(1 + I
p
(FG; B))/G is basic in V(FG)/G provided G is p-mixed.
As consequences, S(FG) and S(FG)/G
p
are both starred or divisible groups.
All of the listed assertions enlarge in a new aspect affirmations established by us in Czechoslovak Math. J. (2002), Math.
Bohemica (2004) and Math. Slovaca (2005) as well. 相似文献
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Describing intermediately fully invariant subgroups of divisible and torsion groups, we show that the intermediately fully invariant subgroups are direct summands in a completely decomposable group whose every homogeneous component is decomposable. For torsion groups, we find out when all their fully invariant subgroups are intermediately fully invariant; and for torsion-free groups, this question comes down to the reduced case. Also, in a torsion group that is the sum of cyclic subgroups, its subgroup is shown to be intermediately inert if and only if it is commensurable with some intermediately fully invariant subgroup. 相似文献