Geodesic
Torsion IF-groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 8, pp. 47-58 
S. Ya. Grinshpon; M. M. Nikolskaya. Torsion IF-groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 8, pp. 47-58. http://geodesic.mathdoc.fr/item/FPM_2012_17_8_a6/
@article{FPM_2012_17_8_a6,
     author = {S. Ya. Grinshpon and M. M. Nikolskaya},
     title = {Torsion {IF-groups}},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {47--58},
     year = {2012},
     volume = {17},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_8_a6/}
}
TY  - JOUR
AU  - S. Ya. Grinshpon
AU  - M. M. Nikolskaya
TI  - Torsion IF-groups
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2012
SP  - 47
EP  - 58
VL  - 17
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/FPM_2012_17_8_a6/
LA  - ru
ID  - FPM_2012_17_8_a6
ER  - 
%0 Journal Article
%A S. Ya. Grinshpon
%A M. M. Nikolskaya
%T Torsion IF-groups
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2012
%P 47-58
%V 17
%N 8
%U http://geodesic.mathdoc.fr/item/FPM_2012_17_8_a6/
%G ru
%F FPM_2012_17_8_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we study torsion groups containing proper fully invariant subgroups isomorphic to the group itself, the so-called IF-groups. We introduce the concept of an admissible sequence of Ulm–Kaplansky invariants for primary groups by use of which a description of IF-groups is obtained in some important classes of $p$-groups.

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

[2] Grinshpon S. Ya., “O stroenii vpolne kharakteristicheskikh podgrupp abelevykh grupp bez krucheniya”, Abelevy gruppy i moduli, 1982, 56–92

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

[4] Fuks L., Beskonechnye abelevy gruppy, v. 1, Mir, M., 1974

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

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

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

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

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

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