The degree of commutativity for group rings
The degree of commutativity for group rings
The degree of commutativity is a classic topic studied in non-commutative algebra. Nevertheless, nowadays is still an active field, with research extending the concept to some specific algebraic structures, or generalizing the concept to infinite groups. The aim of this thesis is to extend the notion of the degree of commutativity for infinite group rings, inspired by some recent results. Particularly, we will prove that the degree of commutativity of an infinite non-commutative group ring is at most $5/8$, and is strictly positive if and only if the group ring is virtually commutative.
Àrees temàtiques de la UPC::Matemàtiques i estadística, Teoria de, Group rings, Classificació AMS::20 Group theory and generalizations::20C Representation theory of groups, Grups, Grups, Teoria de, Noncommutative algebras, group ring, 510, Anells (Àlgebra), Àlgebres no commutatives, Classificació AMS::16 Associative rings and algebras::16S Rings and algebras arising under various constructions, degree of commutativity, Group theory
Àrees temàtiques de la UPC::Matemàtiques i estadística, Teoria de, Group rings, Classificació AMS::20 Group theory and generalizations::20C Representation theory of groups, Grups, Grups, Teoria de, Noncommutative algebras, group ring, 510, Anells (Àlgebra), Àlgebres no commutatives, Classificació AMS::16 Associative rings and algebras::16S Rings and algebras arising under various constructions, degree of commutativity, Group theory
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