This dissertation is devoted to various aspects of groups generated by automata. We study particular classes and examples of such groups from different points of view. It consists of four main parts. In the first part we study Sushchansky p-groups introduced in 1979 by Sushchansky in "Periodic permutation p-groups and the unrestricted Burnside problem". These groups represent one of the earliest examples of Burnside groups and, at the same time, show the potential of the class of groups generated by automata to contain groups with extraordinary properties. The original definition is translated into the language of automata. The original actions of Sushchansky groups on p- ary tree are not level-transitive and we describe their orbit trees. This allows us to simplify the definition and prove that these groups admit faithful level-transitive actions on the same tree. Certain branch structures in their self-similar closures are established. We provide the connection with so-called G groups introduced by Bartholdi, Grigorchuk and Suninc in "Branch groups" that shows that all Sushchansky groups have intermediate growth and allows us to obtain an upper bound on their period growth functions. The second part is devoted to the opposite question of realization of known groups as groups generated by automata. We construct a family of automata with n states, n greater than or equal to 4, acting on a rooted binary tree and generating the free products of cyclic groups of order 2. The iterated monodromy group IMG(z2+i) of the self-map of the complex plain z -> z2 + i is the central object of the third part of dissertation. This group acts faithfully on the binary rooted tree and is generated by 4-state automaton. We provide a self-similar measure for this group giving alternative proof of its amenability. We also compute an L-presentation for IMG(z2+i) and provide calculations related to the spectrum of the Markov operator on the Schreier graph of the action of IMG(z2 + i) on the orbit of a point on the boundary of the binary rooted tree. Finally, the last part is discussing the package AutomGrp for GAP system developed jointly by the author and Yevgen Muntyan. This is a very useful tool for studying the groups generated by automata from the computational point of view. Main functionality and applications are provided.

This dissertation is devoted to the study of self-similar groups and related topics. It consists of three parts. The first part is devoted to the study of examples of finitely generated amenable groups for which every finitely presented cover contains non-abelian free subgroups. The study of these examples was motivated by natural questions about finiteness properties of finitely generated groups. We show that many examples of amenable self-similar groups studied in the literature cannot be covered by finitely presented amenable groups. We investigate the class of contracting self-similar groups from this perspective and formulate a general result which is used to detect this property. As an application we show that almost all known examples of groups of intermediate growth cannot be covered by finitely presented amenable groups. The latter is related to the problem of the existence of finitely presented groups of intermediate growth. The second part focuses on the study of one important example of a self-similar group called the first Grigorchuk group G, from the viewpoint of pro finite groups. We investigate finite quotients of this group related to presentations and group (co)homology. As an outcome of this investigation we prove that the pro finite completion G_hat of this group is not finitely presented as a pro finite group. The last part focuses on a class of recursive group presentations known as L-presentations, which appear in the study of self-similar groups. We investigate the relation of such presentations with the normal subgroup structure of finitely presented groups and show that normal subgroups with finite cyclic quotient of finitely presented groups have such presentations. We apply this result to finitely presented indicable groups without free sub-semigroups.

<p> The mechanisms operating during the metal-assisted growth of III-V nanowires (NWs) by molecular beam epitaxy on (1 1 l)B substrates were investigated through a series of experiments aimed at determining the influence of growth conditions on the morphology and crystal structure. Using GaAs as the principal material system for these studies, it is shown that a good control of these two characteristics can be achieved via a tight control of the temperature, V /III flux ratio, and Ga flux. Low and intermediate growth temperatures of 400°C and 500°C resulted in a strongly tapered morphology, with stacking faults occurring at an average rate of 0.1 nm^(-1). NWs with uniform diameter and the occurrence of crystal defects reduced by more than an order of magnitude were achieved at 600°C, a V /III flux ratio of 2.3, and a Ga impingement rate on the surface of 0.07 nm/s, and suggest the axial growth is group V limited. Increasing the flux ratio favored uniform sidewall growth, thus making the process suitable for the fabrication of core-shell structures. Further observation of steps on the sidewall surface of strongly tapered NWs suggests that radial growth of the shell proceeds in a layer-by-layer fashion, with the edge progressing in a step-flow mode toward the tip. </p> <p> From the experimental considerations, an analytical description of the growth is proposed, based on a simple material conservation model. Direct impingement of growth species on the particle, coupled to their diffusion from the sidewall and the substrate surface, are considered in the derivation of expressions for the time evolution of both axial and radial growths. Factors that take into account the nonunity probability of inclusion of group III adatoms in the axially growing crystal are introduced. Moreover, a step-mediated growth is included to describe the axial evolution of the shell. </p> / Thesis / Doctor of Philosophy (PhD)