Proving Finitely Presented Groups are Large by Computer
نویسندگان
چکیده
منابع مشابه
A Characterisation of Large Finitely Presented Groups
In this paper, we will consider finitely presented groups that have a finite index subgroup which admits a surjective homomorphism onto a non-abelian free group. Gromov called these groups large [4]. Large groups have particularly nice properties (for example, super-exponential subgroup growth). They also play an important rôle in lowdimensional topology: it is a major conjecture that the funda...
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Definition 1. Let G be a group. G is said to be residually finite if the intersection of all normal subgroups of G of finite index in G is trivial. For a survey of results on residual finiteness and related properties, see Mag-nus, Karrass, and Solitar [6, Section 6.5]. We shall present a proof of the following well known theorem, which is important for Kharlampovich [4, 5]. See also O. V. Bele...
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One idea how to prove that a finitely presented group G is infinite is to construct suitable homomorphisms into infinite matrix groups. In [HoP 92] this is done by starting with a finite image H of G and solving linear equations to check whether the epimorphism onto H can be lifted to a representation whose image is an extension of a ZZ-lattice by H, thus exhibiting an infinite abelian section ...
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We prove here that a finitely presented group with a free quotient of rank n is an HNN-extension with n stable letters of a finitely generated group where the associated subgroups are finitely generated. This theorem has a number of consequences. In particular, in the event that the free quotient is cyclic it reduces to an elementary and quick proof of a theorem of Bieri and Strebel. 1. Finitel...
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We establish a general criterion for the finite presentability of subdirect products of groups and use this to characterize finitely presented residually free groups. We prove that, for all n ∈ N, a residually free group is of type FPn if and only if it is of type Fn. New families of subdirect products of free groups are constructed, including the first examples of finitely presented subgroups ...
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ژورنال
عنوان ژورنال: Experimental Mathematics
سال: 2011
ISSN: 1058-6458,1944-950X
DOI: 10.1080/10586458.2011.564540