Determinateness of torsion-free Abelian groups by their holomorphs and almost holomorphic isomorphism
S. Ya. Grinshpona, I. E. Grinshponb
a Tomsk State University
b Tomsk State University of Control Systems and Radioelectronics
In this paper, we study holomorphically isomorphic Abelian groups, i.e., Abelian groups with isomorphic holomorphs. We also study a generalization of the concept of holomorphic isomorphism, namely, almost holomorphic isomorphism, which is deeply connected with normal Abelian subgroups of holomorphs of Abelian groups. Torsion-free Abelian groups that are determined by their holomorphs are highlighted from different classes. In particular, it has been found that any homogeneous separable group can be determined by its holomorph in the class of all Abelian groups.
PDF file (165 kB)
Journal of Mathematical Sciences (New York), 2014, 197:5, 605–613
S. Ya. Grinshpon, I. E. Grinshpon, “Determinateness of torsion-free Abelian groups by their holomorphs and almost holomorphic isomorphism”, Fundam. Prikl. Mat., 17:8 (2012), 35–46; J. Math. Sci., 197:5 (2014), 605–613
Citation in format AMSBIB
\by S.~Ya.~Grinshpon, I.~E.~Grinshpon
\paper Determinateness of torsion-free Abelian groups by their holomorphs and almost holomorphic isomorphism
\jour Fundam. Prikl. Mat.
\jour J. Math. Sci.
Citing articles on Google Scholar:
Related articles on Google Scholar:
|Number of views:|