Geodesic
Abelian groups with nilpotent commutators of endomorphisms
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2012), pp. 60-73 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study classes of abelian groups with nilpotent commutators of their endomorphisms, as well as groups with a semirigid condition imposed on direct summands. We describe these groups amongst separable, vector, and algebraically compact torsion-free groups. We construct examples illustrating the distinction between considered classes of groups, as well as $E$-solvable and $E$-nilpotent groups.
Keywords: commutatorically invariant subgroup, $E$-nilpotent and $E$-solvable groups, power $E$-commutant.
Mots-clés : $E$-engelian group 
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     author = {A. R. Chekhlov},
     title = {Abelian groups with nilpotent commutators of endomorphisms},
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     url = {http://geodesic.mathdoc.fr/item/IVM_2012_10_a4/}
}
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A. R. Chekhlov. Abelian groups with nilpotent commutators of endomorphisms. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2012), pp. 60-73. http://geodesic.mathdoc.fr/item/IVM_2012_10_a4/

[1] Chekhlov A. R., “O kommutatorno invariantnykh podgruppakh abelevykh grupp”, Sib. matem. zhurn., 51:5 (2010), 1163–1174 | MR | Zbl

[2] Chekhlov A. R., “O skobke Li endomorfizmov abelevykh grupp”, Vestn. Tomsk. un-ta. Matem. i mekhan., 2009, no. 2(6), 78–84

[3] Chekhlov A. R., “Ob abelevykh gruppakh s normalnym koltsom endomorfizmov”, Algebra i logika, 48:4 (2009), 520–539 | MR | Zbl

[4] Chekhlov A. R., “Nekotorye primery $E$-razreshimykh grupp”, Vestn. Tomsk. un-ta. Matem. i mekhan., 2010, no. 3(11), 69–76

[5] Chekhlov A. R., “O svoistvakh tsentralno i kommutatorno invariantnykh podgrupp abelevykh grupp”, Vestn. Tomsk. un-ta. Matem. i mekhan., 2009, no. 2(6), 85–99

[6] Krylov P. A., Mikhalev A. V., Tuganbaev A. A., Abelevy gruppy i ikh koltsa endomorfizmov, Faktorial Press, M., 2006

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

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

[9] Tuganbaev A. A., Teoriya kolets. Arifmeticheskie moduli i koltsa, MTsNMO, M., 2009

[10] Grinshpon S. Ya., “O ravenstve nulyu gruppy gomomorfizmov abelevykh grupp”, Izv. vuzov. Matem., 1998, no. 9, 42–46 | MR | Zbl

[11] Chekhlov A. R., “$E$-razreshimye moduli”, Fundament. i prikl. matem., 16:7 (2010), 221–236 | MR

[12] Chekhlov A. R., “O proektivnom kommutante abelevykh grupp”, Sib. matem. zhurn., 53:2 (2012), 451–464