Some combinatorial properties of infinite mono-unary algebras and their applications

Author: Mariami Gobronidze
Keywords: Mono-unary algebra, infinite graph theory, group representation theory, König problem
Annotation:

In master thesis, according to the types of connected components of (A,f) mono-unary algebra types of connected components of (A,f^m) mono-unary algebra is established, in case of f being bijective. Connections between types of connected components of those mono-unary algebras are analyzed. Kőnig’s problem about representation of abstract groups using automorphism group of a graph is discussed. It is proven, that for every infinite G group and every cardinal number α if Card(G)≤ α, there exists a graph with cardinality of α, such that its automorphism group is isomorphic to the G. This essentially strengthens the result of the famous Canadian mathematician Gert Sabidoussi.  

Lecture files:

უსასრულო მონო-უნარული ალგებრების ზოგიერთი კომბინატორული თვისება და მათი გამოყენება [ka]