Hydra group doubles are not residually finite

被引:0
|
作者
Pueschel, Kristen [1 ]
机构
[1] Univ Arkansas, Dept Math, 309 SCEN, Fayetteville, AR 72703 USA
关键词
Residual finiteness; hydra groups; Dehn function; separable subgroup;
D O I
10.1515/gcc-2016-0015
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In 2013, Kharlampovich, Myasnikov, and Sapir constructed the first examples of finitely presented residually finite groups with large Dehn functions. Given any recursive function f, they produce a finitely presented residually finite group with Dehn function dominating f. There are no known elementary examples of finitely presented residually finite groups with super-exponential Dehn function. Dison and Riley's hydra groups can be used to construct a sequence of groups for which the Dehn function of the kth group is equivalent to the kth Ackermann function. Kharlampovich, Myasnikov, and Sapir asked whether or not these groups are residually finite. We show that these constructions do not produce residually finite groups.
引用
收藏
页码:163 / 170
页数:8
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