The characterization of some cyclic groups by the product of element orders.
| Autor: | Shafiei, Hamed, Khosravi, Behrooz, Baniasad Azad, Morteza |
|---|---|
| Předmět: | |
| Zdroj: | Journal of Algebra & Its Applications; Apr2024, Vol. 23 Issue 5, p1-9, 9p |
| Abstrakt: | Let G be a finite group. We denote by ψ ′ (G) the integer ∏ g ∈ G o (g) , where o (g) denotes the order of g ∈ G. It is verified that some finite groups are uniquely determined by their orders and their product of element orders. In this paper, we prove that, if p , q , r , t are different prime numbers, then ℤ p 3 , ℤ p q , ℤ p 2 q and ℤ p q r t are characterized by ψ ′ (G) and if ψ ′ (G) = ψ ′ (ℤ p q r) , then G ≅ A 5 or ℤ p q r . [ABSTRACT FROM AUTHOR] |
| Databáze: | Complementary Index |
| Externí odkaz: |
|