A finitely presented torsion-free simple group

被引:12
作者
Rattaggi, Diego [1 ]
机构
[1] ETH, Dept Math, CH-8092 Zurich, Switzerland
关键词
D O I
10.1515/JGT.2007.028
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We construct a finitely presented torsion-free simple group Sigma(0), acting cocompactly on a product of two regular trees. An infinite family of such groups was introduced by Burger and Mozes [2], [4]. We refine their methods and construct 10 as an index 4 subgroup of a group Sigma < Aut(T-12) x Aut(T-8) presented by 10 generators and 24 short relations. For comparison, the smallest virtually simple group of [4, Theorem 6.4] needs more than 18000 relations, and the smallest simple group constructed in [4, 6.5] needs even more than 360000 relations in any finite presentation.
引用
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页码:363 / 371
页数:9
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