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This article is cited in 28 scientific papers (total in 28 papers)
On subgroup distortion in finitely presented groups
A. Yu. Ol'shanskii M. V. Lomonosov Moscow State University
Abstract:
It is proved that every computable function $G\to \mathbb N=\{0,1,\dots\}$ on a group $G$ (with certain necessary restrictions) can be realized up to equivalence as a length function of elements by embedding $G$ in an appropriate finitely presented group. As an example, the length of $g^n$, the $n$th power of an element $g$ of a finitely presented group, can grow as $n^{\theta }$ for each computable $\theta \in (0,1]$. 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.
Received: 01.04.1997
Citation:
A. Yu. Ol'shanskii, “On subgroup distortion in finitely presented groups”, Mat. Sb., 188:11 (1997), 51–98; Sb. Math., 188:11 (1997), 1617–1664
Linking options:
https://www.mathnet.ru/eng/sm276https://doi.org/10.1070/sm1997v188n11ABEH000276 https://www.mathnet.ru/eng/sm/v188/i11/p51
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Abstract page: | 465 | Russian version PDF: | 265 | English version PDF: | 19 | References: | 48 | First page: | 1 |
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