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Jan Jakubik 《Czechoslovak Mathematical Journal》2005,55(4):917-922
In this paper it is proved that an abelian lattice ordered group which can be expressed as a nontrivial lexicographic product
is never affine complete.
This work was supported by VEGA grant 2/1131/21. 相似文献
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S. Ya. Grinshpon 《Acta Appl Math》2005,85(1-3):143-146
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Graham A. Niblo 《Journal of Algebra》1999,220(2):185
We show that residually finite or word hyperbolic groups which can be decomposed as a finite union of double cosets of a cyclic subgroup are necessarily virtually cyclic, and we apply this result to the study of Frobenius permutation groups. We show that in general, finite double coset decompositions of a group can be interpreted as an obstruction to splitting a group as a free product with amalgamation or an HNN extension. 相似文献
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In the paper, Problem 18.3 of the book “Abelian groups” (2015) by L. Fuchs is solved in the case of Abelian groups with finite p-ranks. For an Abelian group A, a sequence of groups (An) is considered, where A0 = A and An+1 = End An. It is shown that, if all p-ranks of the group A are finite, then this sequence can stabilize either after A0 or after A1.
相似文献8.
A proof is given of the following theorem, which characterizesfull automorphism groups of ordered abelian groups: a groupH is the automorphism group of some ordered abelian group ifand only if H is right-orderable. 2000 Mathematics Subject Classification20K15, 20K20, 20F60, 20K30 (primary); 03E05 (secondary). 相似文献
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An abelian group A is an S-group (S +-group) if every subgroup B ≤ A of finite index is A-generated (A-solvable). This article discusses some of the differences between torsion-free S-groups and mixed S-groups, and studies (mixed) S- and S +-groups, which are self-small and have finite torsion-free rank. 相似文献
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The structure of the additive group of a regular module is considered. Abelian groups that are regular modules over their rings of endomorphisms are studied. Nonreduced endoregular groups and endoregular torsion-free groups of finite rank are described. 相似文献
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V. Kh. Farukshin 《Journal of Mathematical Sciences》2014,197(5):684-687
A representation for p-local Abelian torsion-free groups of finite rank is obtained in terms of homomorphisms of p-adic modules of finite rank with fixed basis. 相似文献
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Mathematical Notes - A group is said to be homomorphically stable with respect to another group if the union of the homomorphic images of the first group in the second group is a subgroup of the... 相似文献
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A. R. Chekhlov 《Journal of Mathematical Sciences》2014,197(5):708-733
E-nilpotent and E-solvable Abelian groups are studied. The properties of such groups are studied, and examples illustrating the differences and connections between the investigated classes of groups are presented. The structure of E-solvable periodical, completely decomposable, coperiodic, split mixed, and other groups is shown. 相似文献
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Mike Develin 《Annals of Combinatorics》2002,6(3-4):295-312
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E. I. Kompantseva 《Journal of Mathematical Sciences》2014,197(5):625-634
It is known that in an Abelian group G that contains no nonzero divisible torsion-free subgroups the intersection of upper nil-radicals of all the rings on G is $\bigcap\limits_{p} pT(G)$ , where T(G) is the torsion part of G. In this work, we define a pure fully invariant subgroup G*???T(G) of an arbitrary Abelian mixed group G and prove that if G contains no nonzero torsion-free subgroups, then the subgroup $\bigcap\limits_{p} pG^{*}$ is a nil-ideal in any ring on G, and the first Ulm subgroup G1 is its nilpotent ideal. 相似文献