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Showing 1 to 20 of 24 for “"Free groups"”.
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Rigidity in free groups
Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-04-14T19:42:44Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 thesis-ex.tex: 173754 bytes, checksum: c5da772624d2323106ae5ec8436ca1b3 (MD5) Ray_Brian.pdf: 417963 bytes, checksum: …
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Some Model Theory of Free Groups
… results, both pertaining to the model theory of free groups. In the first set of results, we prove that non-abelian free groups of finite rank at least 3 or of countable rank are not A-homogeneous. We then build on the proof of this result to show that two classes of groups, namely finitely …
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Forcing ℵ1-free groups to be free.
ℵ1-free groups, abelian groups whose countable subgroups are free, are objects of both algebraic and set-theoretic interest. Illustrating this, we note that ℵ1-free groups, and in particular the question of when ℵ1-free groups are free, were central to the resolution of the Whitehead problem as …
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Free groups and the axiom of choice
The Nielsen–Schreier theorem states that subgroups of free groups are free. As all of its proofs use the Axiom of Choice, it is natural to ask whether the theorem is equivalent to the Axiom of Choice. Other questions arise in this context, such as whether the same is true for free abelian groups, …
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Graphs Of Free Groups And Their Measure Equivalence.
… Group Theory of an interesting class of groups that can be obtained as graphs of free groups. These groups are called Quadratic Baumslag-Solitar groups, and are defined by graphs of groups that have infinite cyclic edge groups, and whose vertex groups are either infinite cyclic, or …
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Matrix Representations of Automorphism Groups of Free Groups
… theory of the automorphism group Aut (Fn) of a free group by studying the representation theory of three finite subgroups: two symmetric groups, Sn and Sn+1, and a Coxeter group of type Bn, also known as a hyperoctahedral group. The representation theory of these subgroups is well understood in …
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An Algebraic Generalization of Integration in Free Groups
Made available in DSpace on 2014-12-14T13:09:29Z (GMT). No. of bitstreams: 1 7616212.pdf: 1960818 bytes, checksum: e98d736a9670ac265633caa75c365e3c (MD5) Previous issue date: 1976
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Some Results on Free Groups in Combinatorial Group Theory
Let Fm be a free group of a finite rank m ≥ 2. We prove that there exist two elements u 1, u2 ∈ Fm such that every endomorphism y of Fm with non-cyclic image is completely determined by y (u1), y (u2). We obtain this result as a corollary of the construction of a C-test word vn( x1,...,xn), …
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Length bounds for the conjugacy search problem in relatively hyperbolic groups, limit groups and residually free groups
… conjugacy length bounds for several classes of groups. We use geometric and algebraic methods to show that there is a polynomial conjugacy length bound for relatively hyperbolic groups, a linear multiple conjugacy length bound for limit groups, and a polynomial multiple conjugacy length bound …
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Groups in Which Commutativity Is a Transitive Relation
… dissertation is concerned with the class of CT-groups. Finite and locally finite CT-groups are studied in detail with structure theorems given in both solvable and insolvable cases. The investigation of solvable CT-groups leads naturally to the study of fixed-point-free groups of automorphisms …
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Solving Algorithmic Problems in Finitely Presented Groups via Machine Learning
… successfully applied to algorithmic problems in free groups. In this dissertation, we seek to extend these techniques to finitely presented non-free groups, in particular to polycyclic and metabelian groups that are of interest to non-commutative cryptography.</p> <p>As a prototypical example, we …
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Combinatorial models for surface and free group symmetries
… closed curves. Similar complexes of spheres, free factors, and free splittings allow combinatorial representation of the automorphisms of a free group. We consider a Birman exact sequence for combinatorial models of mapping class groups and free group automorphisms. We apply this and other …
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Separability within alternating groups and randomness
This thesis promotes known residual properties of free groups, surface groups, right angled Coxeter groups and right angled Artin groups to the situation where the quotient is only allowed to be an alternating group. The proofs follow two related threads of ideas. The first thread leads to …
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Solutions of Quadratic Equations in Small Cancellation Groups
… equations in small cancellation quotients of free groups and free products. Paul E. Schupp has obtained similar results for a restricted class of quadratic equations (those without constants). Some of the methods used here were previously employed by Leo P. Comerford and Charles C. Edmunds in …
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Certain free group functions and untangling closed curves on surfaces
… index functions for finitely generated free groups. In joint work with Ilya Kapovich we obtain lower bounds for these functions and relate these free group results back to the setting of hyperbolic surfaces. Chapters 1-6 in parts comprise of a joint paper with Kapovich that is under …
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Spaces of homomorphisms and group cohomology
… of view. The case in which the source group is a free abelian group of rank n is studied in more detail since this space can be identified with the space of commuting n-tuples of elements from G. This latter case is of particular interest when the target is a Lie group. The simplicial approach …
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Extending partial isomorphisms
… classes of topological similarity in the groups of automorphisms of some linearly ordered Fraisse classes: the rationals, the linearly ordered random graph and the linearly ordered Urysohn space. The main theorem establishes meagerness of two-dimensional similarity classes in these groups. …
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Computations and lower bounds for scl and the relative Gromov seminorm
… of stable commutator length, an invariant of groups that measures homological complexity and is connected to several notions of negative curvature in geometric group theory. A first aspect of this is to give exact computations, motivated by questions of rationality. A particular case of …
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Dynamics of free group automorphisms and a subgroup alternative for out(fn)
… we prove several structural theorems for subgroups of Out(F_N).
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Graph products of groups
… 1970's Baudisch introduced the idea of the semifree group, that is, a group in which the only relators are commutators of generators. Baudisch was mainly concerned with subgroup problems, employing length arguments on the elements of these groups. More recently Droms and Servatius have continued …
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