TORSION-FREE WEAKLY TRANSITIVE ABELIAN GROUPS

REFERENCES

• Arnold , D. ( 1980 ). Finite Rank Torsion-Free Abelian Groups and Rings . Lecture Notes in Mathematics 931 . Berlin : Springer-Verlag .
   Google Scholar
• Carroll , D. , Goldsmith , B. ( 1996 ). On transitive and fully transitive abelian. p-groups . Proc. Royal Irish Academy 96A : 33 – 41 .
   Google Scholar
• Corner , A. L. S. ( 1976 ). The independence of Kaplansly's notions of transitivity and full transitivity . Quart. J. Math. Oxford 27 : 15 – 20 .
   Google Scholar
• Corner , A. L. S. , Göbel , R. (1985). Prescribing endomorphism algebras–-a unified treatment. Proc. London Math. Soc. 50:447–479.
   Google Scholar
• Dedekind , R. , Dirichlet , R.G. ( 1968 ). Zahlentheorie . New York : Chelsea .
   Google Scholar
• Dobrusin , Yu. B. ( 1985 ). Extensions of partial endomorphisms of torsion-free abelian groups . Abelian Groups and Modules. Tomsk: Tomsk. Gos. Univ. , pp. 36 – 59 .
   Google Scholar
• Dugas , M. , Mader , A. , Vinsonhaler , C. ( 1987 ). Large E -rings exist . J. Alg. 108 : 88 – 101 . [CROSSREF]
   Web of Science ®Google Scholar
• Dugas , M. , Shelah , S. ( 1989 ). E -transitive groups in L. Abelian Group Theory . Am. Math. Soc. pp. 191 – 199 .
   Google Scholar
• Files , S. ( 1996 ). On trasitive mixed abelian groups Abelian Group Theory: Proceedings of the International Conference at Colorado Springs. Lecture Notes in Pure and Applied Mathematics 182 . pp. 243 – 251 .
   Google Scholar
• Files , S. ( 1997 ). Transitivity and full transitivity for nontorsion modules . J. Alg. 197 : 468 – 478 . [CROSSREF]
   Google Scholar
• Files , S. , Goldsmith , B. ( 1998 ). Transitive and fully transitive groups . Proc. Am. Math. Soc. 126 : 1605 – 1610 . [CROSSREF]
   Google Scholar
• Fuchs , L. ( 1970, 1973 ). Infinite Abelian Groups . Vols. I and II . Academic Press .
   Google Scholar
• Goldsmith , B. Strüngmann , L. Torsion weakly transitive abelian groups. In preparation .
   Google Scholar
• Griffith , P. ( 1968 ). Transitive and fully transitive primary abelian groups . Pacific J. Math. 25 : 249 – 254 .
   Google Scholar
• Grinshpon , S. Ya. ( 1982 ). On the structure of fully characteristic subgroups of abelian torsion-free groups . Abelian Groups and Modules. Tomsk: Tomsk. Gos. Univ. , pp. 56 – 92 .
   Google Scholar
• Grinshpon , S. Ya. , Misyakov , V. M. ( 1991 ). Full transitivity of direct products of abelian groups . Abelian Groups and Modules. Tomsk: Tomsk. Gos. Univ. , pp. 23 – 30 .
   Google Scholar
• Grinshpon , S. Ya., Misyakov , V. M. ( 1986 ). Fully transitive abelian groups Abelian Groups and Modules. Tomsk: Tomsk. Gos. Univ. , pp. 12 – 27 .
   Google Scholar
• Grove , L. ( 1983 ). Algebra . Pure and Applied Mathematics . Academic Press .
   Google Scholar
• Hausen , J. ( 1987 ). E -transitive torsion-free abelian groups . J. Alg. 107 : 17 – 27 . [CROSSREF]
   Google Scholar
• Hennecke , G. ( 1999 ). Transitivitätseigenschaften abelscher p -Gruppen. Doctoral thesis, Essen University .
   Google Scholar
• Hennecke , G. Strüngmann , L. ( 2000 ). Transitivity and full transitivity for p-local modules . Archiv der Mathematik 74 : 321 – 329 . [CROSSREF]
   Google Scholar
• Hill , P. ( 1969 ). On transitive and fully transitive primary groups . Proc. Am. Math. Soc. 22 : 414 – 417 .
   Web of Science ®Google Scholar
• Kaplansky , I. ( 1954, 1969 ). Infinite Abelian Groups . Ann Arbor : University of Michigan Press .
   Google Scholar
• Krylov , P. A. ( 1989 ). Strongly homogeneous torsion-free abelian groups . Sibirsk. Mat. Zh. 24 : 77 – 84 .
   Google Scholar
• Krylov , P. A. ( 1986 ). Irreducible abelian groups and their endomorphism rings . Abelian Groups and Modules. Tomsk: Tomsk. Gos. Univ. , pp. 73 – 100 .
   Google Scholar
• Mader , A. ( 2000 ). Almost Completely Decomposable Abelian Groups . Algebra Logic and Applications 13 . Gordont and Breach .
   Google Scholar
• Meehan , C. Strüngmann , L. Rational rings related to weakly transitive torsion-free groups. To appear .
   Google Scholar
• Megibben , C. ( 1966 ). Large subgroups and small homomorphisms . Michigan Mathematical Journal 13 : 153 – 160 . [CROSSREF]
   Google Scholar
• Misyakov , V. M. ( 1993 ). Full transitivity of reduced abelian groups . Abelian Groups and Modules. Tomsk: Tomsk. Gos. Univ. , pp. 134 – 156 .
   Google Scholar
• Paras , A. Strü ngmann , L. ( 2003 ). Fully transitive, p -groups with finite first Ulm subgroup . Proc. Am. Math. Soc. 131 : 371 – 377 . [CROSSREF]
   Google Scholar
• #Communicated by K. Rangaswamy.
   Google Scholar