Geodesic
Totally Transitive Torsion-Free Groups of Finite $p$-Rank
Algebra i logika, Tome 40 (2001) no. 6, pp. 698-715.

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Totally transitive torsion-free groups all non-zero endomorphisms of which are monomorphisms are studied. Such are characterized in terms of modules over some rings with specific properties. Also, a structural description is provided for quasihomogeneous, totally transitive, torsion-free groups $A$ of finite $p$-rank, for at least one prime $p$ not dividing $A$.
Keywords: totally transitive torsion-free group, quasihomogeneous totally transitive group
Mots-clés : endomorphism, monomorphism. 
@article{AL_2001_40_6_a4,
     author = {A. R. Chekhlov},
     title = {Totally {Transitive} {Torsion-Free} {Groups} of {Finite} $p${-Rank}},
     journal = {Algebra i logika},
     pages = {698--715},
     publisher = {mathdoc},
     volume = {40},
     number = {6},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2001_40_6_a4/}
}
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A. R. Chekhlov. Totally Transitive Torsion-Free Groups of Finite $p$-Rank. Algebra i logika, Tome 40 (2001) no. 6, pp. 698-715. http://geodesic.mathdoc.fr/item/AL_2001_40_6_a4/