Residual properties of groups defined by basic commutators

被引：1

作者：

Baumslag, Gilbert ^{[1
,2
]}

Mikhailov, Roman ^{[3
,4
]}

机构：

[1] CUNY City Coll, CAISS, New York, NY 10031 USA

[2] CUNY City Coll, Dept Comp Sci, New York, NY 10031 USA

[3] St Petersburg State Univ, Chebyshev Lab, St Petersburg 199178, Russia

[4] Steklov Math Inst, St Petersburg Dept, St Petersburg 191023, Russia

来源：

GROUPS GEOMETRY AND DYNAMICS | 2014年 / 8卷 / 03期

基金：

美国国家科学基金会;

关键词：

Commutator calculus; residual nilpotence; basic commutators; one-relator groups; NILPOTENT GROUPS; CENTRAL SERIES; PRODUCTS; ORDER;

D O I：

10.4171/GGD/242

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the residual nilpotence of groups defined by basic commutators. We prove that the so-called Hydra groups as well as certain of their generalizations and quotients are, in the main, residually torsion-free nilpotent. By way of contrast we give an example of a group defined by two basic commutators which is not residually torsion-free nilpotent.

引用

页码：621 / 642

页数：22

共 35 条

[1] ON RESIDUAL NILPOTENCE OF CERTAIN ONE-RELATOR GROUPS [J].

BAUMSLAG, G .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1968, 21 (05) :491-&

[2] GROUPS WITH SAME LOWER CENTRAL SEQUENCE AS A RELATIVELY FREE GROUP .I. GROUPS [J].

BAUMSLAG, G .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 129 (02) :308-&

[3] Finitely generated residually torsion-free nilpotent groups. I [J].

Baumslag, G .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1999, 67 :289-317

[4]

Baumslag G., 1962, MATH Z, V78, P423, DOI [10.1007/BF01195185, DOI 10.1007/BF01195185]

[5]

Baumslag G., 1971, LECT NOTES NILPOTENT

[6]

Baumslag G., UNPUB

[7]

Baumslag G., 2013, ARXIV13014629MATHGR

[8] Recognizing powers in nilpotent groups and nilpotent images of free groups [J].

Baumslag, Gilbert .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2007, 83 :149-155

[9] SOME REFLECTIONS ON PROVING GROUPS RESIDUALLY TORSION-FREE NILPOTENT. I [J].

Baumslag, Gilbert .

ILLINOIS JOURNAL OF MATHEMATICS, 2010, 54 (01) :315-325

[10]

Bousfield A. K., 1977, MEM AM MATH SOC, V10

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