Geodesic
Indecomposable $p$-local torsion-free groups with quadratic and cubic splitting fields
Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 5, pp. 17-29.

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Indecomposable torsion-free $p$-local Abelian groups of finite rank with quadratic and cubic splitting field $K$ are characterized. As a consequence, for groups with quadratic splitting field $K$ it is proved that $K$-decomposable $p$-local torsion-free Abelian groups of finite rank are isomorphic if and only if their endomorphism rings are isomorphic. 
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S. V. Vershina. Indecomposable $p$-local torsion-free groups with quadratic and cubic splitting fields. Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 5, pp. 17-29. http://geodesic.mathdoc.fr/item/FPM_2015_20_5_a2/

[1] Vershina S. V., “Gruppy rasschepleniya nerazlozhimykh $p$-lokalnykh grupp bez krucheniya”, Algebra i logika: teoriya i prilozheniya, Materialy mezhdunarodnoi konf., posvyaschennoi 80-letiyu V. P. Shunkova (Krasnoyarsk, 2013), 25–26

[2] Ivanov A. M., “Ob odnom svoistve $p$-servantnykh podgrupp gruppy tselykh $p$-adicheskikh chisel”, Matem. zametki, 27:6 (1980), 859–867 | MR | Zbl

[3] Farukshin V. Kh., “Lokalnye abelevy gruppy bez krucheniya”, Fundament. i prikl. matem., 17:8 (2011/2012), 147–152

[4] Fomin A. A., “Tenzornoe proizvedenie abelevykh grupp bez krucheniya”, Sib. matem. zhurn., 16:4 (1975), 869–878 | MR

[5] Fuks L., Beskonechnye abelevy gruppy, v. 1, Mir, M., 1974; v. 2, 1977

[6] Arnold D. M., Dugas M., “Co-purely indecomposable modules over discrete valuation rings”, J. Pure Appl. Algebra, 161:1–2 (2001), 1–12 | DOI | MR | Zbl

[7] Arnold D. M., Dugas M., “Indecomposable modules over Nagata valuation domains”, Proc. Amer. Math. Soc., 122:3 (1994), 689–696 | DOI | MR | Zbl

[8] Arnold D. M., Dugas M., Rangaswamy K. M., “Finite rank Butler groups and torsion-free modules over a discrete valuation ring”, Proc. Amer. Math. Soc., 129 (2001), 325–335 | DOI | MR | Zbl

[9] Farukshin V. Kh., “Local Abelian torsion-free groups”, J. Math. Sci., 195:5 (2014), 684–687 | DOI | MR

[10] Lady E. L., “Splitting fields for torsion-free modules over discrete valuation rings. I”, J. Algebra, 49:1 (1977), 261–275 | DOI | MR | Zbl

[11] Lady E. L., “Splitting fields for torsion-free modules over discrete valuation rings. II”, J. Algebra, 66 (1980), 281–306 | DOI | MR | Zbl

[12] Lady E. L., “Splitting fields for torsion-free modules over discrete valuation rings. III”, J. Algebra, 66 (1980), 307–320 | DOI | MR | Zbl

[13] Zanardo P., “Kurosch invariants for torsion-free modules over Nagata valuation domains”, J. Pure Appl. Algebra, 82 (1992), 195–209 | DOI | MR | Zbl