Wharton, Elizabeth (2006) The model theory of certain infinite soluble groups. PhD thesis, University of Oxford.

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Abstract
This thesis is concerned with aspects of the model theory of infinite soluble groups. The results proved lie on the border between group theory and model theory: the questions asked are of a modeltheoretic nature but the techniques used are mainly grouptheoretic in character.
We present a characterization of those groups contained in the universal closure of a restricted wreath product U wr G, where U is an abelian group of zero or finite squarefree exponent and G is a torsionfree soluble group with a bound on the class of its nilpotent subgroups. For certain choices of G we are able to use this characterization to prove further results about these groups; in particular, results related to the decidability of their universal theories.
The latter part of this work consists of a number of independent but related topics.
We show that if G is a finitely generated abelian bymetanilpotent group and H is elementarily equivalent to G then the subgroups and are elementarily equivalent, as are the quotient groups and .
We go on to consider those groups universally equivalent to , where the free groups of the variety are residually finite pgroups for infinitely many primes p, distinguishing between the cases when c = 1 and when c > 2.
Finally, we address some important questions concerning the theories of free groups in product varieties , where is a nilpotent variety whose free groups are torsionfree; in particular we address questions about the decidability of the elementary and universal theories of such groups. Results mentioned in both of the previous two
paragraphs have applications here.
Item Type:  Thesis (PhD) 

Subjects:  H  N > Mathematical logic and foundations D  G > Group theory and generalizations 
Research Groups:  Algebra Research Group Mathematical Logic Group 
ID Code:  1461 
Deposited By:  Eprints Administrator 
Deposited On:  02 Feb 2012 16:19 
Last Modified:  29 May 2015 19:09 
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