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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Quotient-Transitivity And Cyclic Subgroup-Transitivity, Brendan Goldsmith, Ketao Gong
Quotient-Transitivity And Cyclic Subgroup-Transitivity, Brendan Goldsmith, Ketao Gong
Articles
We introduce two new notions of transitivity for Abelian π-groups based on isomorphism of quotients rather than the classical use of equality of height sequences associated with Abelian π-group theory. Unlike the classical theory where βmostβ groups are transitive, these new notions lead to much smaller classes, but even these classes are sufficiently large to be interesting.
Some Transitivity-Like Concepts In Abelian Groups, Gabor Braun, Brendan Goldsmith, Ketao Gong, Lutz Strungmann
Some Transitivity-Like Concepts In Abelian Groups, Gabor Braun, Brendan Goldsmith, Ketao Gong, Lutz Strungmann
Articles
The classical notions of transitivity and full transitivity in Abelian p-groups have natural extensions to concepts called Krylov and weak transitivity. The interconnections between these four types of transitivity are determined for Abelian p-groups; there is a marked difference in the relationships when the prime p is equal to 2. In the final section the relationship between full and Krylov transitivity is examined in the case of mixed Abelian groups which are p-local in the sense that multiplication by an integer relatively prime to p is an automorphism.
Some Transitivity Results For Torsion Abelian Groups, Brendan Goldsmith, Lutz Strungmann
Some Transitivity Results For Torsion Abelian Groups, Brendan Goldsmith, Lutz Strungmann
Articles
We introduce a new class of fully transitive and transitive Abelian p-groups and study the new concept of weak transitivity which is the missing link between full transitivity and transitivity.
Torsion-Free Weakly Transitive Abelian Groups, Brendan Goldsmith, Lutz Strungmann
Torsion-Free Weakly Transitive Abelian Groups, Brendan Goldsmith, Lutz Strungmann
Articles
We introduce the notion of weak transitivity for torsion-free abelian groups. A torsion-free abelian group G is called weakly transitive if for any pair of elements x, y β G and endomorphisms Ο, Ο β End(G) such that xΟ = y, yΟ = x, there exists an automorphism of G mapping x onto y. It is shown that every suitable ring can be realized as the endomorphism ring of a weakly transitive torsion-free abelian group, and we characterize up to a number-theoretical property the separable weakly transitive torsion-free abelian groups.
On Torsion And Mixed Minimal Abelian Groups, Brendan Goldsmith, S. O. Hogain
On Torsion And Mixed Minimal Abelian Groups, Brendan Goldsmith, S. O. Hogain
Articles
An abelian group is said to be minimal if it is isomorphic to all its subgroups of finite index. We obtain a complete characterisation of such groups in the torsion case; in the case of mixed groups of rank 1 we obtain a characterisation for some large classes of such groups.