$FP_\infty$ groups and HNN extensions
نویسندگان
چکیده
منابع مشابه
On Groups which contain no HNN-Extensions
A group is called HNN-free if it has no subgroups that are nontrivial HNN-extensions. 23 We prove that finitely generated HNN-free implies virtually polycyclic for a large class of groups. We also consider finitely generated groups with no free subsemigroups of rank 2 25 and show that in many situations such groups are virtually nilpotent. Finally, as an application of our results, we determine...
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An extraordinary theorem of Gromov, [4], characterizes the finitely generated groups of polynomial growth; a group has polynomial growth iff it is nilpotent by finite. This theorem went a long way from its roots in the class of discrete subgroups of solvable Lie groups. Wolf, [11], proved that a polycyclic group of polynomial growth is nilpotent by finite. This theorem is primarily about linear...
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The most useful constructions in Combinatorial Group Theory are amalgamated free products and HNN-extensions, and they are the two basic examples in the theory of graphs of groups due to Bass and Serre (see [9]). We recall that given a group G and a subgroup H 6 G together with monomorphisms (respectively homomorphisms) ψ, φ : H −→ G, the group determined by the presentation 〈 G, t; t−1ψ(h)t = ...
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It is shown that the knapsack problem, which was introduced by Myasnikov et al. for arbitrary finitely generated groups, can be solved in NP for graph groups. This result even holds if the group elements are represented in a compressed form by SLPs, which generalizes the classical NP-completeness result of the integer knapsack problem. We also prove general transfer results: NP-membership of th...
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is called an ascending HNN extension of G (or the mapping torus of the endomorphism φ). In particular, the ascending HNN extensions of free groups of finite rank are simply the groups given by presentations 〈x1, ..., xn, t | txit−1 = wi, i = 1, ..., n〉, where w1, ..., wn are words generating a free subgroup of rank n. In [BS], Borisov and Sapir proved that all ascending HNN extensions of linear...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1983
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1983-15165-0