Abelian Groups with Nilpotent Commutators of Endomorphisms

被引：6

作者：

Chekhlov, A. R. ^{[1
]}

机构：

[1] Tomsk State Univ, Pr Lenina 36, Tomsk 634050, Russia

来源：

RUSSIAN MATHEMATICS | 2012年 / 56卷 / 10期

关键词：

commutatorically invariant subgroup; E-nilpotent and E-solvable groups; E-engelian group; power E-commutant;

D O I：

10.3103/S1066369X12100052

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 among 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.

引用

页码：50 / 61

页数：12

共 12 条

[1]

Chekhlov AR, 2009, VESTN TOMSK GOS U-MA, P85

[2]

Chekhlov AR, 2010, VESTN TOMSK GOS U-MA, P69

[3]

[Чехлов Андрей Ростиславович Chekhlov A.R.], 2009, [Алгебра и логика, Algebra i logika], V48, P520

[4]

Chekhlov A. R., 2009, VESTNIK TOMSK U MATE, V2, P78

[5]

CHEKHLOV AR, 2010, FUNDAMENT PRIKL MATE, V16, P221

[6]

CHEKHLOV AR, 2012, SIB MAT ZH, V53, P451

[7]

CHEKHLOV AR, 2010, SIB MAT ZH, V51, P1163

[8]

Fuchs L., 1970, INFINITE ABELIAN GRO, V1

[9]

Fuchs L., 1973, INFINITE ABELIAN GRO

[10]

Grinshpon S.Ya., 1998, RUSSIAN MATH TZ VUZ, V42, P39

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