Geodesic
Torsion IF-groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 8, pp. 47-58.

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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. 
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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/

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