Full transitivity of Abelian groups

Misyakov, V. M.

doi:10.1007/s10958-008-9177-1

Cited by 4 publications

(2 citation statements)

References 21 publications

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“…For sufficiently wide classes of -groups this topic is treated in [3][4][5][6][7] and in other papers. The works [8][9][10][11][12][13] and others are dedicated to the investigation of this question in torsion-free and mixed groups. p A group A is called a cotorsion group if its extension by means of any torsion-free group splits, i.e., C   , C A Ext 0  .…”

Section: Introductionmentioning

confidence: 99%

The Lattice of Fully Invariant Subgroups of the Cotorsion Hull

Kemoklidze¹

2013

APM

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The paper considers the lattice of fully invariant subgroups of the cotorsion hull T  when a separable primary group is an arbitrary direct sum of torsion-complete groups.The investigation of this problem in the case of a cotorsion hull is important because endomorphisms in this class of groups are completely defined by their action on the torsion part and for mixed groups the ring of endomorphisms is isomorphic to the ring of endomorphisms of the torsion part if and only if the group is a fully invariant subgroup of the cotorsion hull of its torsion part. In the considered case, the cotorsion hull is not fully transitive and hence it is necessary to introduce a new function which differs from an indicator and assigns an infinite matrix to each element of the cotorsion hull. The relation difined on the set T   of these matrices is different from the relation proposed by the autor in the countable case and better discribes the lower semilattice . The use of the relation essentially simplifies the verification of the required properties. It is proved that the lattice of fully invariant subgroups of the group T   is isomorphic to the lattice of filters of the lower semilattice  .

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Section: Introductionmentioning

confidence: 99%

The Lattice of Fully Invariant Subgroups of the Cotorsion Hull

Kemoklidze¹

2013

APM

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“…is an increasing sequence of ordinal numbers and symbols ∞ satisfying the following condition: if between σ n and σ n+1 there is a jump, then in A there is an element of order p and height σ n (see [3,Theorem 67.1]]. Also, with the use of terms of the indicator and full transitivity, the lattice of the fully invariant subgroup was studied for some classes of torsion-free mixed and p-groups by Baer [1], Göbel [4], Grinshpon and Krylov [6], Kaplansky [7], Linton [10], Mader [11], Misyakov [13], Moore and Hewet [14], Moskalenko [15], Piere [16], and others. Little is known on the lattice of fully invariant subgroups in the class of cotorsion groups.…”

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confidence: 99%