Finite presentation of fibre products of metabelian groups

被引：8

作者：

Baumslag, G

Bridson, MR

Holt, DF

Miller, CF

机构：

[1] Math Inst, Oxford OX1 3LB, England

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

[3] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England

[4] Univ Melbourne, Dept Math & Stat, Parkville, Vic 3052, Australia

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2003年 / 181卷 / 01期

关键词：

SUBGROUPS;

D O I：

10.1016/S0022-4049(02)00307-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that if Gamma is a finitely presented metabelian group, then the "untwisted" fibre product or pull-back P associated to any short exact sequence 1 --> N --> Gamma --> Q --> 1 is again finitely presented. In contrast, if N and Q are abelian, then the analogous "twisted" fibre-product is not finitely presented unless F is polycyclic. Also a number of examples are constructed, including a non-finitely presented metabelian group P with H-2(P,Z) finitely generated. (C) 2003 Elsevier Science B.V. All rights reserved.

引用

页码：15 / 22

页数：8

共 7 条

[1]

BAUMSLAG G, 1984, J LOND MATH SOC, V30, P44

[2] Fibre products, non-positive curvature, and decision problems [J].

Baumslag, G ;

Bridson, MR ;

Miller, CF ;

Short, H .

COMMENTARII MATHEMATICI HELVETICI, 2000, 75 (03) :457-477

[3]

BIERI R, 1980, P LOND MATH SOC, V41, P439

[4]

BIERI R, 1981, J REINE ANGEW MATH, V322, P170

[5] The subgroups of direct products of surface groups [J].

Bridson, MR ;

Howie, J ;

Miller, CF ;

Short, H .

GEOMETRIAE DEDICATA, 2002, 92 (01) :95-103

[6]

Brown K. S., 1982, GRADUATE TEXTS MATH, V87

[7]

GRUNEWALD FJ, 1978, J LOND MATH SOC, V17, P427

← 1 →