TITLE:
On the Full Transitivity of a Cotorsion Hull of the Pierce Group
AUTHORS:
Tariel Kemoklidze
KEYWORDS:
Full Transitivity of a Group; Cotorsion Hull; Fully Invariant Subgroup
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.4 No.3,
March
28,
2014
ABSTRACT:
The paper
considers the problem of full transitivity of a cotorsion hull of a separable primary group G when a ring of
endomorphisms E(G) of the group G has the form , where Es(G) is a subring of small endomorphisms of the
ring E(G), whereas Jp is a ring of integer P-adic numbers. Investigation of
the issue of full transitivity of a group is essentially helpful in studying
its fully invariant subgroups as well as the lattice formed by these subgroups.
It is proved that in the considered case, the cotorsion hull is not fully
transitive. A lemma is proposed, which can be used in the study of full
transitivity of a group and in other cases.