Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Συρίγος Διονύσιος
Supervisors info:
Ολυμπία Ταλέλλη Καθηγ. (Επιβλέπουσα), Ευάγγελος Ράπτης Καθηγ., Μιχάλης Συκιώτης Επίκ. Καθηγ.
Original Title:
Προσεγγιστικά Πεπερασμένες ΗΝΝ-επεκτάσεις πολυκυκλικών ομάδων
Translated title:
Ascending HNN extensions of polyclic groups are residually finite
Summary:
The main result of this dissertation is the fact that the ascending HNN
extensions of polycyclic-by-fi nite groups are residually nite. Since many
constructions preserve residual finiteness (for example free products, direct
products) is interesting to know if it is preserved by ascending HNN extensions.
The answer is negative and it the final chapter of the dissertation,
there is a counterexample of a f.g. residually finite group which has an
ascending
HNN extension that it isn't residually finite. The answer is positive,
as we have mentioned before for polycyclic-by- finite groups, but later it is
proved something more general, in particular that the answer is positive for
f.g. linear groups (this class includes polycyclic, free and metabelian).
Keywords:
Polycyclic, Ascending HNN extensions, Residually finite
