This dissertation is devoted to the groups generated by automata. The first
part of the dissertation deals with L-presentations for such groups. We describe the
sufficient condition for an essentially free automaton group to have an L-presentation.
We also find the L-presentation for several other groups generated by three-state
automata, and we describe the defining relations in the Grigorchuk groups G_w. In
case when the sequence w is almost periodic these relations provide an L-presentation
for the group G_w. We also describe defining relations in the series of groups which
contain Grigorchuk-Erschler group and the group of iterated monodromies of the
polynomial z^2 + i.
The second part of the dissertation considers groups generated by 3-state automata
over the alphabet of 2 letters and 2-state automata over the 3-letter alphabet.
We continue the classification work started by the research group at Texas A&M
University ([BGK+07a, BGK+07b]) and further reduce the number of pairwise nonisomorphic
groups generated by 3-state automata over the 2-letter alphabet. We also
study the groups generated by 2-state automata over the 3-letter alphabet and obtain
a number of classification results for this class of group.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2009-05-751 |
| Date | 16 January 2010 |
| Creators | Muntyan, Yevgen |
| Contributors | Grigorchuk, Rostislav, Nekrashevych, Volodymyr |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation |
| Format | application/pdf |
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