Primary $IF$-groups
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 3 (2011), pp. 25-31 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this work, we study primary groups containing proper fully invariant subgroups isomorphic to the group, the so-called $IF$-groups. We define the admissible sequence of Ulm–Kaplansky invariants for primary groups. Using these sequences, $IF$-groups are described in some important classes of $p$-groups.
Mots-clés : $IF$-group, torsion complete group
Keywords: fully invariant subgroup, Ulm–Kaplansky invariants, admissible sequence.
@article{VTGU_2011_3_a3,
     author = {S. Ya. Grinshpon and M. M. Nikolskaya},
     title = {Primary $IF$-groups},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {25--31},
     year = {2011},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2011_3_a3/}
}
TY  - JOUR
AU  - S. Ya. Grinshpon
AU  - M. M. Nikolskaya
TI  - Primary $IF$-groups
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2011
SP  - 25
EP  - 31
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VTGU_2011_3_a3/
LA  - ru
ID  - VTGU_2011_3_a3
ER  - 
%0 Journal Article
%A S. Ya. Grinshpon
%A M. M. Nikolskaya
%T Primary $IF$-groups
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2011
%P 25-31
%N 3
%U http://geodesic.mathdoc.fr/item/VTGU_2011_3_a3/
%G ru
%F VTGU_2011_3_a3
S. Ya. Grinshpon; M. M. Nikolskaya. Primary $IF$-groups. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 3 (2011), pp. 25-31. http://geodesic.mathdoc.fr/item/VTGU_2011_3_a3/

[1] Beaumont R. A., Pierce R. S., “Isomorphic direct summands of abelian groups”, Math. Annalen., 153 (1964), 21–37 | DOI | MR

[2] Monk G. S., “Abelian p-groups without proper isomorphic pure dense subgroups”, Ill. J. Math., 14:1 (1970), 164–177 | MR | Zbl

[3] Goldsmith B., Ohogain S., Wallutis S., “Quasi-minimal groups”, Proc. Amer. Math. Soc., 132:8 (2004), 2185–2195 | DOI | MR | Zbl

[4] Grinshpon S. Ya., Nikolskaya (Savinkova) M. M., “IF-gruppy”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2010, no. 1(9), 5–14

[5] Benabdallah K. M., Eisenstadt B. J., Irwin J. M., Poluianov E. W., “The structure of large subgroups of primary Abelian groups”, Acta Math. Acad. Scient. Hung., 21:3–4 (1970), 421–435 | DOI | MR | Zbl

[6] Fuks L., Beskonechnye abelevy gruppy, v. 2, Mir, M., 1977, 416 pp.

[7] Pierce R. S., “Homomorphisms of primary Abelian groups”, Topics in Abelian Groups, Chicago, 1963, 215–310 | MR

[8] Fuks L., Beskonechnye abelevy gruppy, v. 1, Mir, M., 1974, 336 pp.

[9] Kulikov L. Ya., “K teorii abelevykh grupp proizvolnoi moschnosti”, Mat. sb., 16(58):2 (1945), 129–162 | MR | Zbl

[10] Grinshpon S. Ya., “O nekotorykh klassakh primarnykh abelevykh grupp pochti izomorfnykh po vpolne kharakteristicheskim podgruppam”, Izv. vuzov. Matematika, 1976, no. 2, 23–30 | MR | Zbl