On subgroup distortion in finitely presented groups
On subgroup distortion in finitely presented groups
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有限群中的子群畸变
DOI：
10.1070/sm1997v188n11abeh000276
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发表时间：
1997
影响因子：
0.8
通讯作者：
A. Ol’shanskii
中科院分区：
文献类型：
--
作者：
A. Ol’shanskii
证明了群上的每一个可计算函数（在一定的必要条件下），通过嵌入到适当的有限表示群中，都可以等价地实现为元素的长度函数。作为一个例子，长度，一个有限表示的群的元素的次幂，可以随着每一个可计算的增长而增长。这回答了Gromov b[2]的一个问题。主要工具是本文建立的希格曼嵌入的改进版本，它保留了元素的长度。
It is proved that every computable function on a group (with certain necessary restrictions) can be realized up to equivalence as a length function of elements by embedding in an appropriate finitely presented group. As an example, the length of , the th power of an element of a finitely presented group, can grow as for each computable . This answers a question of Gromov [2]. The main tool is a refined version of the Higman embedding established in this paper, which preserves the lengths of elements.