THE TWISTED TWIN OF THE GRIGORCHUK GROUP

被引：14

作者：

Bartholdi, Laurent ^{[1
]}

Siegenthaler, Olivier ^{[2
]}

机构：

[1] Univ Gottingen, Math Inst, D-37073 Gottingen, Germany

[2] ETH, Dept Math, CH-8092 Zurich, Switzerland

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2010年 / 20卷 / 04期

关键词：

Self-similar group; automata group; group acting on tree; torsion group; just-infinite group; endomorphic presentation; Schur multiplier; congruence property;

D O I：

10.1142/S0218196710005728

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a twisted version of Grigorchuk's first group, and stress its similarities and differences to its model. In particular, we show that it admits a finite endomorphic presentation, has infinite-rank multiplier, and does not have the congruence property.

引用

页码：465 / 488

页数：24

共 17 条

[1]

[Anonymous], 1985, MAT ZAMETKI

[2] Endomorphic presentations of branch groups [J].

Bartholdi, L .

JOURNAL OF ALGEBRA, 2003, 268 (02) :419-443

[3]

BARTHOLDI L, 2009, ISR J MATH IN PRESS

[4]

BARTHOLDI L, 2008, DUKE MATH J IN PRESS

[5] A NILPOTENT QUOTIENT ALGORITHM FOR CERTAIN INFINITELY PRESENTED GROUPS AND ITS APPLICATIONS [J].

Bartholdi, Laurent ;

Eick, Bettina ;

Hartung, Rene .

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2008, 18 (08) :1321-1344

[6]

GRIGORCHUK, 1980, Funktsional. Anal. i Prilozhen., V14, P53, DOI DOI 10.1007/BF01078416

[7]

Grigorchuk R. I., 2000, PROG MATH, P121

[8]

GRIGORCHUK RI, 1983, DOKL AKAD NAUK SSSR+, V271, P30

[9]

GRIGORCHUK RI, 1997, GROUPS ST ANDREWS 19, V1, P290

[10]

Holt D., 2009, KBMAG KNUTH BENDIX M

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