In this note we show that a group with a finite number of elements of maximal order must be finite. In other words, there are no infinite groups with finitely many elements of maximal order. In ...

Let G be a finite group, p a prime, and x a p-element in G. An element g in G is called a witness of G if the subgroup generated by x and g is a p-group. The set of all witnesses of x in G is denoted ...

Group theory serves as a fundamental language for describing symmetry in both mathematics and physics. Finite groups, defined by their limited number of elements, are central to modern algebra and ...

Finite group: A group with a finite number of elements. Power graph: A graph where vertices represent elements of a group and an edge connects two vertices if one is an integral power of the other.