Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science

2013-02-26

2013

Καρασούλου Άννα

Ευάγγελος Ράπτης Καθηγ. (Επιβλέπων), Δημήτριος Βάρσος Καθηγ., Μιχαήλ Συκιώτης Επικ. Καθηγ.

Το πρόβλημα του Tarski για ελεύθερες ομάδες

Greek

Tarski's problem for free groups

The purpose of this work is mainly the presentation of Tarski's problem on the
elementary theory of the free groups and all of the prerequisite knowledge to
make it understandable. Firstly, we define free groups, free products,
HNN-extensions and prove their basic properties. Then we present graphs of
groups and develop the theory of group actions on trees. This theory offers a
topological view of free products and HNN-extensions. Also, if X is a proper
geodesic metric space and G a group acting with isometries co-compactly and
discretely on X, we prove that G is finitely generated and X is
quasi-isometric with the Cayley graph of G. This theorem is one of the
fundamental results of geometric group theory. An overview about hyperbolic
groups is also provided and we conclude with a presentation of Tarski's
problem, focusing on limit groups and Makanin-Razborov diagrams.

Geometric group theory, Hyperbolic groups, Tarski's problem

No

0

Yes

16

74

File access is restricted.

https://pergamos.lib.uoa.gr/uoa/dl/object/1320454