The Word Problem in Groups of Cohomological
نویسندگان
چکیده
We show that the finitely presented groups with unsolvable word problem given by the Boone-Britton construction have cohomological dimension 2. More precisely we show these groups can be obtained from a free group by successively forming HNN-extensions where the associated subgroups are finitely generated free groups. Also the presentations obtained for these groups are aspherical. Using this we show there is no algorithm to determine whether a presentation is aspherical. There is no algorithm to determine whether a finite 2-complex is aspherical.
منابع مشابه
A Cohomological Characterization of Hyperbolic Groups
A finitely presented group G is word hyperbolic iff H2 (∞) (G, l∞) = 0. §
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