Portal de Periódicos da CAPES

On the structure of finite groups determined by the arithmetic and geometric means of element orders

2024; Taylor & Francis; Volume: 52; Issue: 7 Linguagem: Inglês

10.1080/00927872.2024.2305283

1532-4125

Valentina Grazian, Carmine Monetta, Marialaura Noce,

Coding theory and cryptography

In this paper we consider two functions related to the arithmetic and geometric means of element orders of a finite group, showing that certain lower bounds on such functions strongly affect the group structure. In particular, for every prime p, we prove a sufficient condition for a finite group to be p-nilpotent, that is, a group whose elements of p′-order form a normal subgroup. Moreover, we characterize finite cyclic groups with prescribed number of prime divisors.