Geodesic
Finite automorphism groups of torsion-free Abelian groups of finite rank
Izvestiya. Mathematics, Tome 32 (1989) no. 3, pp. 501-521 
S. F. Kozhukhov. Finite automorphism groups of torsion-free Abelian groups of finite rank. Izvestiya. Mathematics, Tome 32 (1989) no. 3, pp. 501-521. http://geodesic.mathdoc.fr/item/IM2_1989_32_3_a2/
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     title = {Finite automorphism groups of torsion-free {Abelian} groups of finite rank},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Abelian torsion-free groups of finite rank with finite automorphism groups are considered as rigid extensions of a system of strongly indecomposable groups $A_j$, $j=1,\dots,k$, of finite rank and having finite automorphism groups, by a finite $p$-group $P$. Such groups are called $(A,p)$-groups. The author introduces for $(A,P)$-groups the concept of $(A,P)$-type, which represents a choice of $k$ integer matrices. A complete description of $(A,P)$-groups is given by means of $(A,P)$-types. Using this description, a series of problems on finite groups of automorphisms of torsion-free abelian groups of finite rank are solved. Furthermore, it is shown that the actual solution of any one of these problems comes down to a question of the consistency of a system of equations of the first degree modulo $p^t$, where $p^t$ is the maximal order of elements of $P$. Bibliography: 11 titles.

[1] Jonsson B., “On direct decompositions of torsion free abelian groups”, Math. Scand., 1959, no. 7, 361–371 | MR

[2] Lady E. L., “Almost completely decomposable torsion free abelian groups”, Proc. Amer. Math. Soc., 45:1 (1974), 41–47 | DOI | MR | Zbl

[3] Kozhukhov S. F., “Abelevy gruppy bez nilpotentnykh endomorfizmov”, Abelevy gruppy i moduli, Tomsk, 1979, 87–94

[4] Kozhukhov S. F., “Ob odnom klasse pochti vpolne razlozhimykh abelevykh grupp bez krucheniya”, Izv. vuzov. Matematika, 1983, no. 10, 29–36 | MR | Zbl

[5] Burdhardt R., “Elementary Abelian extensions of finite rigid systems”, Commun. Algebra, 11:13 (1983), 1473–1499 | DOI | MR

[6] Kozhukhov S. F., “Pochti vpolne razlozhimye abelevy gruppy bez krucheniya s primarnymi faktorami”, Abelevy gruppy i moduli, Tomsk, 1985, 42–55

[7] Kozhukhov S. F., “O rasshireniyakh abelevykh grupp bez krucheniya”, Materialy 18 Vsesoyuzn. algebraicheskoi konf., tezisy soobsch., t. 1, Kishinev, 1985, 261

[8] Fuks L., Beskonechnye abelevy gruppy, t. 1, Mir, M., 1974

[9] Fuks L., Beskonechnye abelevy gruppy, t. 2, Mir, M., 1977

[10] Kozhukhov S. F., Gruppy avtomorfizmov regulyarno polnykh abelevykh grupp, Dep. v VINITI No 2790-77, TGU, Tomsk

[11] Kozhukhov S. F., “Prodolzhenie avtomorfizmov v pochti vpolne razlozhimykh abelevykh gruppakh bez krucheniya”, Abelevy gruppy i moduli, Tomsk, 1982, 117–127