Results 11 to 20 of about 35,005 (235)
Summands of finite rank torsion free abelian groups
Journal of Algebra, 1974 AbstractA finite rank torsion free abelian group has, up to isomorphism, only finitely many summands.
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Dualities for torsion-free abelian groups of finite rank
Journal of Algebra, 1990 All groups considered here are torsion-free abelian groups of finite rank. Let F be a full free subgroup of such a group G. The finite outer type of G, FOT(G), is \((...,\pi_ p,...)\), where \(p^{\pi_ p}\) is the order of a maximal cyclic summand in the p-component of the reduced part of G/F.
Vinsonhaler, C, Wickless, W
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Strongly Homogeneous Torsion Free Abelian Groups of Finite Rank [PDF]
Proceedings of the American Mathematical Society, 1976 An abelian group is strongly homogeneous if for any two pure rank 1 subgroups there is an automorphism sending one onto the other. Finite rank torsion free strongly homogeneous groups are characterized as the tensor product of certain subrings of algebraic number fields with finite direct sums of isomorphic subgroups of Q Q , the ...
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Discussiones Mathematicae - General Algebra and Applications, 2017 It is studied how rank two pure subgroups of a torsion-free Abelian group of rank three influences its structure and type set. In particular, the criterion for such a subgroup B to be a direct summand of a torsion-free Abelian group of rank three with ...
Najafizadeh Alireza, Woronowicz Mateusz
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Finitely generated abelian groups of units [PDF]
, 2019 In 1960 Fuchs posed the problem of characterizing the groups which are the groups of units of commutative rings. In the following years, some partial answers have been given to this question in particular cases.
Del Corso, Ilaria
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Fully inert subgroups of divisible Abelian groups [PDF]
, 2013 A subgroup H of an Abelian group G is said to be fully inert if the quotient (H + phi(H)/H is finite for every endomorphism phi of G. Clearly, this is a common generalization of the notions of fully invariant, finite and finite-index subgroups.
Dikranjan, Dikran +3 more
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Homogeneity and prime models in torsion-free hyperbolic groups [PDF]
, 2010 We show that any nonabelian free group $F$ of finite rank is homogeneous; that is for any tuples $\bar a$, $\bar b \in F^n$, having the same complete $n$-type, there exists an automorphism of $F$ which sends $\bar a$ to $\bar b$.
Houcine, Abderezak Ould
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Frobenius groups of automorphisms and their fixed points [PDF]
, 2010 Suppose that a finite group $G$ admits a Frobenius group of automorphisms $FH$ with kernel $F$ and complement $H$ such that the fixed-point subgroup of $F$ is trivial: $C_G(F)=1$.
Belyaev V. V. +10 more
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A Cancellation Criterion for Finite-Rank Torsion-Free Abelian Groups [PDF]
Proceedings of the American Mathematical Society, 1985 In this paper, a necessary ring-theoretical criterion is given for a finite-rank torsion-free abelian group to have the cancellation property. This generalizes results obtained by L. Fuchs and F. Loonstra [5] for the rank-one case and resolves the cancellation problem for strongly indecomposable groups.
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Cohomology and profinite topologies for solvable groups of finite rank [PDF]
, 2012 Assume $G$ is a solvable group whose elementary abelian sections are all finite. Suppose, further, that $p$ is a prime such that $G$ fails to contain any subgroups isomorphic to $C_{p^\infty}$.
Lorensen, Karl
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