On the Full Transitivity of a Cotorsion Hull of the Pierce Group

ABSTRACT

The paper
considers the problem of full transitivity of a cotorsion hull of a separable primary group ** G** when a ring of
endomorphisms

Cite this paper

Kemoklidze, T. (2014) On the Full Transitivity of a Cotorsion Hull of the Pierce Group.*Advances in Pure Mathematics*, **4**, 76-81. doi: 10.4236/apm.2014.43012.

Kemoklidze, T. (2014) On the Full Transitivity of a Cotorsion Hull of the Pierce Group.

References

[1] Fuchs, L. (1970) Infinite Abelian Groups. I. Pure and Applied Mathematics, Vol. 36, Academic Press, New York.

[2] Fuchs, L. (1973) Infinite Abelian Groups. II. Pure and Applied Mathematics, Vol. 36-II, Academic Press, New York.

[3] May, W. and Toubassi, E. (1976) Endomorphisms of Abelian Groups and the Theorem of Baer and Kaplansky. Journal of Algebra, 43, 1-13. http://dx.doi.org/10.1016/0021-8693(76)90139-3

[4] Baer, R. (1935) Type of Elements and Characteristic Subgroups of Abelian Groups. Proceedings of the London Mathematical Society, Series 2, 39, 481-514. http://dx.doi.org/10.1112/plms/s2-39.1.481

[5] Kaplansky, I. (1969) Infinite Abelian Groups. The University of Michigan Press, Ann Arbor.

[6] Linton, R.S. (1976) On Fully Invariant Subgroups of Primary Abelian Groups. Michigan Mathematical Journal, 22, 281-284. http://dx.doi.org/10.1307/mmj/1029001528

[7] Moore, J.D. and Hewett, E.J. (1971/72) On Fully Invariant Subgroups of Abelian p-Groups. Commentarii Mathematici Universitatis Sancti Pauli, 20, 97-106.

[8] Gobel, R. (1974) The Characteristic Subgroups of the Baer-Specker Group. Mathematische Zeitschrift, 140, 289-292.

http://dx.doi.org/10.1007/BF01214169

[9] Grinshpon, S.Ya. and Krylov, P.A. (2005) Fully Invariant Subgroups, Full Transitivity, and Homomorphism Groups of Abelian Groups. Journal of Mathematical Sciences, 128, 2894-2997. http://dx.doi.org/10.1007/s10958-005-0245-5

[10] Mader, A. (1970) The Fully Invariant Subgroups of Reduced Algebraically Compact Groups. Publicationes Mathematicae Debrecen, 17, 299-306.

[11] Moskalenko, A.I. (1989) Cotorsion Hull of a Separable Group. Algebra i Logika, 28, 207-226.

http://dx.doi.org/10.1007/BF01979377

[12] Kemoklidze, T. (2013) The Lattice of Fully Invariant Subgroups of the Cotorsion Hull. Advances in Pure Mathematics, 3, 670-697. http://www.emis.de/journals/GMJ/vol13/contents.htm http://dx.doi.org/10.4236/apm.2013.38090

[13] Kemoklidze, T. (2006) On the Full Transitivity of a Cotorsion Hull. Georgian Mathematical Journal, 13, 79-84.

[14] Pierce, R.S. (1963) Homomorphisms of Primary Abelian Groups. In: Topics in Abelian Groups, Scott, Foresman and Co., Chicago, 215-310.

[15] Stringall, R.W. (1967) Endomorphism Rings of Primary Abelian Groups. Pacific Journal of Mathematics, 20, 535-557.

http://dx.doi.org/10.2140/pjm.1967.20.535

[1] Fuchs, L. (1970) Infinite Abelian Groups. I. Pure and Applied Mathematics, Vol. 36, Academic Press, New York.

[2] Fuchs, L. (1973) Infinite Abelian Groups. II. Pure and Applied Mathematics, Vol. 36-II, Academic Press, New York.

[3] May, W. and Toubassi, E. (1976) Endomorphisms of Abelian Groups and the Theorem of Baer and Kaplansky. Journal of Algebra, 43, 1-13. http://dx.doi.org/10.1016/0021-8693(76)90139-3

[4] Baer, R. (1935) Type of Elements and Characteristic Subgroups of Abelian Groups. Proceedings of the London Mathematical Society, Series 2, 39, 481-514. http://dx.doi.org/10.1112/plms/s2-39.1.481

[5] Kaplansky, I. (1969) Infinite Abelian Groups. The University of Michigan Press, Ann Arbor.

[6] Linton, R.S. (1976) On Fully Invariant Subgroups of Primary Abelian Groups. Michigan Mathematical Journal, 22, 281-284. http://dx.doi.org/10.1307/mmj/1029001528

[7] Moore, J.D. and Hewett, E.J. (1971/72) On Fully Invariant Subgroups of Abelian p-Groups. Commentarii Mathematici Universitatis Sancti Pauli, 20, 97-106.

[8] Gobel, R. (1974) The Characteristic Subgroups of the Baer-Specker Group. Mathematische Zeitschrift, 140, 289-292.

http://dx.doi.org/10.1007/BF01214169

[9] Grinshpon, S.Ya. and Krylov, P.A. (2005) Fully Invariant Subgroups, Full Transitivity, and Homomorphism Groups of Abelian Groups. Journal of Mathematical Sciences, 128, 2894-2997. http://dx.doi.org/10.1007/s10958-005-0245-5

[10] Mader, A. (1970) The Fully Invariant Subgroups of Reduced Algebraically Compact Groups. Publicationes Mathematicae Debrecen, 17, 299-306.

[11] Moskalenko, A.I. (1989) Cotorsion Hull of a Separable Group. Algebra i Logika, 28, 207-226.

http://dx.doi.org/10.1007/BF01979377

[12] Kemoklidze, T. (2013) The Lattice of Fully Invariant Subgroups of the Cotorsion Hull. Advances in Pure Mathematics, 3, 670-697. http://www.emis.de/journals/GMJ/vol13/contents.htm http://dx.doi.org/10.4236/apm.2013.38090

[13] Kemoklidze, T. (2006) On the Full Transitivity of a Cotorsion Hull. Georgian Mathematical Journal, 13, 79-84.

[14] Pierce, R.S. (1963) Homomorphisms of Primary Abelian Groups. In: Topics in Abelian Groups, Scott, Foresman and Co., Chicago, 215-310.

[15] Stringall, R.W. (1967) Endomorphism Rings of Primary Abelian Groups. Pacific Journal of Mathematics, 20, 535-557.

http://dx.doi.org/10.2140/pjm.1967.20.535