I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2002, VOLUME 8, NUMBER 2, PAGES 407-473
Fully invariant subgroups of Abelian groups and full transitivity
S. Ya. Grinshpon
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An Abelian group is said to be fully
transitive if for any elements with
are the height-matrices of elements
there exists an endomorphism of sending into .
We say that an Abelian group is -group if any fully
invariant subgroup of has the form ,
where is some -matrix with ordinal
numbers and symbol for entries.
The description of fully transitive groups and -groups in various
classes of Abelian groups is obtained.
The results of this paper show that every -group is
a fully transitive group, but there are fully transitive torsion
free groups and mixed groups, which are not -groups.
The full description of fully invariant subgroups and their lattice
for fully transitive groups in various classes of Abelian groups is
All articles are
published in Russian.
Last modified: November 26, 2002