Starting from properties of the commutativity graph of a group, we deal with two group theoretical classes containing all abelian groups: the class of commutative-transitive groups and that of power-commutative groups. We aim at collecting the main known results concerning the structure of these groups. Moreover, we give the definition of the commutative-transitive kernel and of the power-commutative kernel of any group. Finally, we point out properties of such kernels for some classes of groups.

On certain group theoretical properties generalizing commutativity

DELIZIA, Costantino
;
NICOTERA, Chiara
2006-01-01

Abstract

Starting from properties of the commutativity graph of a group, we deal with two group theoretical classes containing all abelian groups: the class of commutative-transitive groups and that of power-commutative groups. We aim at collecting the main known results concerning the structure of these groups. Moreover, we give the definition of the commutative-transitive kernel and of the power-commutative kernel of any group. Finally, we point out properties of such kernels for some classes of groups.
2006
0821837117
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/1870356
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