Title: Finitely presentable subgroups and algorithms
Abstract: We show that there is a finitely presented group G for which there is no algorithm that takes a finitely presentable subgroup H of G, an abstract finite presentation Q for H, and constructs an isomorphism between Q and H. To do this, we show that there is a finitely presented group with solvable word problem (namely, the Baumslag-Solitar group BS(2,3)) for which there is no algorithm that takes a recursive presentation of that same group, and solves the word problem in the recursive presentation. Our main result suggests, but does not prove, that there is a genuine difference between strong effective coherence and weak effective coherence.
Publication Year: 2011
Publication Date: 2011-09-08
Language: en
Type: preprint
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Cited By Count: 1
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