Finite automorphism groups of torsion-free Abelian groups of finite rank
Izvestiya. Mathematics , Tome 32 (1989) no. 3, pp. 501-521.

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.
@article{IM2_1989_32_3_a2,
     author = {S. F. Kozhukhov},
     title = {Finite automorphism groups of torsion-free {Abelian} groups of finite rank},
     journal = {Izvestiya. Mathematics },
     pages = {501--521},
     publisher = {mathdoc},
     volume = {32},
     number = {3},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1989_32_3_a2/}
}
TY  - JOUR
AU  - S. F. Kozhukhov
TI  - Finite automorphism groups of torsion-free Abelian groups of finite rank
JO  - Izvestiya. Mathematics 
PY  - 1989
SP  - 501
EP  - 521
VL  - 32
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1989_32_3_a2/
LA  - en
ID  - IM2_1989_32_3_a2
ER  - 
%0 Journal Article
%A S. F. Kozhukhov
%T Finite automorphism groups of torsion-free Abelian groups of finite rank
%J Izvestiya. Mathematics 
%D 1989
%P 501-521
%V 32
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1989_32_3_a2/
%G en
%F IM2_1989_32_3_a2
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/

[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