The group PSL(2,q) is not the multiplication group of a loop |
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Authors: | Ari Vesanen |
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Institution: | Department of Mathematics , University of Oulu , Oulu, Finland, 90570 |
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Abstract: | ABSTRACT 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 ∈ G and endomorphisms ?, ψ ∈ End(G) such that x? = y, yψ = 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. |
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Keywords: | Full transitivity Transitivity |
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