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Probabilistic and Monte Carlo Simulations,e show that it is indeed possible for a sublattice subgroup of . to have no irreducible elements and still be transitive on the set of pairs . < . in .. This answers a question raised in “The first-order theory of .-permutation groups”, a Conference talk by the first author.

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Properties of Abelian Groups Determined by Their Endomorphism Ringles over arbitrary rings, the second half focuses mainly on the case of torsion-free Abelian groups. Although there are many applications of endomorphism rings to the theory of mixed Abelian groups, a comprehensive discussion of this subject is beyond the framework of a survey article. In particular

stratum-corneum

礼节

Rigid ℵ1-Free Abelian Groups with Prescribed Factors and Their Role in the Theory of Cellular Coverslian groups with prescribed torsion-free kernels and co-kernels. In particular, the method was applied to the class of .-free abelian groups in order to complement results from Rodríguez–Strüngmann (Mediterr. J. Math. 6:139–150, 2010) and Göbel–Rodríguez–Strüngmann (Fundam. Math. 217:211–231, 2012).

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thalamus

On Subsets and Subgroups Defined by Commutators and Some Related Questionsommutators identities, subsets defined by autocommutators. We are interested in conditions under which each of these sets forms a subgroup of .. In particular we continue the investigation started by L.C. Kappe and R.F. Morse on the subset of all commutators in .. Furthermore, we present some recent

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Proclaim

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Countable 1-Transitive Trees., Proc Lond Math Soc 58:454–494, 1989), and on lower 1-transitive linear orders (Barbina and Chicot, Towards a classification of the countable 1-transitive trees: countable lower 1-transitive linear orders. arXiv:1504.03372), all in the countable case. We lead on from these to give a complete descr

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On Ore’s Theorem and Universal Words for Permutations and Injections of Infinite Setsving infinitely many infinite orbits (and no others). This implies Ore’s influential theorem that each permutation of . is a commutator, a similar result due to Mesyan for the injections of ., and a result on which injections . of . can be written in the form . = .. ⋅ ...