S. Ya. Grinshpon, M. M. Nikol'skaya (Savinkova), “<nobr>$IF$</nobr>-groups”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2010, Number 1(9),Pages <nobr>5

This article is cited in 3 papers

MATHEMATICS

$IF$-groups

S. Ya. Grinshpon^a, M. M. Nikol'skaya (Savinkova)^ba

^a Tomsk State University, Faculty of Mechanics and Mathematics
^b Tomsk State University of Architecture and Building

Abstract: In this paper we study $IF$-groups, i.e., groups containing proper fully invariant subgroups isomorphic to the group itself. We prove some general properties of $IF$-groups and establish the connection between separable $IF$-groups and their basic subgroups. Torsion complete $IF$-groups are described in detail.

Keywords: $IF$-group, fully invariant subgroup, wide subgroup, Ulm-Kaplansky invariants, torsion complete group.

UDC: 512.541

Accepted: February 10, 2010