FUNDAMENTALNAYA
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

Abstract

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An Abelian group $A$ is said to be fully
transitive if for any elements $a,b$Î A with
$H(a)$£
H(b)
($H(a)$, $H(b)$
are the height-matrices of elements
$a$
and $b$)
there exists an endomorphism of $A$ sending $a$ into $b$.
We say that an Abelian group $A$ is $H$-group if any fully
invariant subgroup $S$ of $A$ has the form $S\; =\; \{a$Î A
| H(a) ³ M},
where $M$ is some $$w ´ w-matrix with ordinal
numbers and symbol $$¥ for entries.
The description of fully transitive groups and $H$-groups in various
classes of Abelian groups is obtained.
The results of this paper show that every $H$-group is
a fully transitive group, but there are fully transitive torsion
free groups and mixed groups, which are not $H$-groups.
The full description of fully invariant subgroups and their lattice
for fully transitive groups in various classes of Abelian groups is
obtained.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k02/k022/k02205h.htm

Last modified: November 26, 2002