Quasi-isomorphism invariants for two classes of finite rank Butler groups

Authors:
D. Arnold and C. Vinsonhaler

Journal:
Proc. Amer. Math. Soc. **118** (1993), 19-26

MSC:
Primary 20K15

MathSciNet review:
1157997

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Abstract: A complete set of numerical quasi-isomorphism invariants is given for a class of torsion-free abelian groups containing all groups of the form , where is an -tuple of subgroups of the additive rationals and is the cokernel of the diagonal embedding . This classification and its dual include, as special cases, earlier classifications of strongly indecomposable groups of the form and their duals.

**[ARV]**D. Arnold, F. Richman, and C. Vinsonhaler,*Representations of finite posets and valuated groups*, J. Algebra**155**(1993), no. 1, 110–126. MR**1206624**, 10.1006/jabr.1993.1033**[AV1]**D. Arnold and C. Vinsonhaler,*Representing graphs for a class of torsion-free abelian groups*, Abelian group theory (Oberwolfach, 1985) Gordon and Breach, New York, 1987, pp. 309–332. MR**1011321****[AV2]**D. Arnold and C. Vinsonhaler,*Quasi-isomorphism invariants for a class of torsion-free abelian groups*, Houston J. Math.**15**(1989), no. 3, 327–340. MR**1032393****[AV3]**D. Arnold and C. Vinsonhaler,*Invariants for a class of torsion-free abelian groups*, Proc. Amer. Math. Soc.**105**(1989), no. 2, 293–300. MR**935102**, 10.1090/S0002-9939-1989-0935102-X**[AV4]**D. M. Arnold and C. I. Vinsonhaler,*Duality and invariants for Butler groups*, Pacific J. Math.**148**(1991), no. 1, 1–10. MR**1091526****[AV5]**D. Arnold and C. Vinsonhaler,*Pure subgroups of finite rank completely decomposable groups. II*, Abelian group theory (Honolulu, Hawaii, 1983) Lecture Notes in Math., vol. 1006, Springer, Berlin, 1983, pp. 97–143. MR**722614**, 10.1007/BFb0103698**[AV6]**D. M. Arnold and C. I. Vinsonhaler,*Invariants for classes of indecomposable representations of finite posets*, J. Algebra**147**(1992), no. 1, 245–264. MR**1154682**, 10.1016/0021-8693(92)90260-S**[AV7]**D. M. Arnold and C. I. Vinsonhaler,*Isomorphism invariants for abelian groups*, Trans. Amer. Math. Soc.**330**(1992), no. 2, 711–724. MR**1040040**, 10.1090/S0002-9947-1992-1040040-5**[AV8]**-,*Finite rank Butler groups, a survey of recent results*, Proceedings of the Curacao Conference on Abelian groups (to appear).**[FM]**Laszlo Fuchs and Claudia Metelli,*On a class of Butler groups*, Manuscripta Math.**71**(1991), no. 1, 1–28. MR**1094735**, 10.1007/BF02568390**[HM]**Paul Hill and Charles Megibben,*The classification of certain Butler groups*, J. Algebra**160**(1993), no. 2, 524–551. MR**1244926**, 10.1006/jabr.1993.1199**[La]**E. L. Lady,*Extension of scalars for torsion free modules over Dedekind domains*, Symposia Mathematica, Vol. XXIII (Conf. Abelian Groups and their Relationship to the Theory of Modules, INDAM, Rome, 1977) Academic Press, London-New York, 1979, pp. 287–305. MR**565611****[Le]**W. Y. Lee,*Co-representing graphs for a class of torsion-free abelian groups*, Ph.D. thesis, New Mexico State Univ., 1986.**[R]**Fred Richman,*An extension of the theory of completely decomposable torsion-free abelian groups*, Trans. Amer. Math. Soc.**279**(1983), no. 1, 175–185. MR**704608**, 10.1090/S0002-9947-1983-0704608-X

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DOI:
https://doi.org/10.1090/S0002-9939-1993-1157997-0

Article copyright:
© Copyright 1993
American Mathematical Society