dc.contributor.advisor | Grigorchuk, Rostislav | |
dc.contributor.advisor | Nekrashevych, Volodymyr | |
dc.creator | Muntyan, Yevgen | |
dc.date.accessioned | 2010-01-16T00:10:57Z | |
dc.date.available | 2010-01-16T00:10:57Z | |
dc.date.created | 2009-05 | |
dc.date.issued | 2010-01-16 | |
dc.identifier.uri | https://hdl.handle.net/1969.1/ETD-TAMU-2009-05-751 | |
dc.description.abstract | 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. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | en_US | |
dc.subject | automata | en |
dc.subject | automata groups | en |
dc.subject | groups | en |
dc.subject | finitely generated groups | en |
dc.title | Automata groups | en |
dc.type | Book | en |
dc.type | Thesis | en |
thesis.degree.department | Mathematics | en |
thesis.degree.discipline | Mathematics | en |
thesis.degree.grantor | Texas A&M University | en |
thesis.degree.name | Doctor of Philosophy | en |
thesis.degree.level | Doctoral | en |
dc.contributor.committeeMember | Rojas, Maurice | |
dc.contributor.committeeMember | Butenko, Sergiy | |
dc.contributor.committeeMember | Sunik, Zoran | |
dc.type.genre | Electronic Dissertation | en |