Characterization of finite groups by a bijection with a divisible property on the element orders. Issue 8 (3rd August 2017) - Jafarian Amiri, Seyyed Majid; Amiri, Mohsen
ABSTRACT: Let G be a finite solvable group of order n and p be a prime divisor of n . In this article, we prove that if the Sylow p -subgroup of G is neither cyclic nor generalized quaternion, then there exists a bijection f from G onto the abelian groupC n p × C p such that for each x ∈ G, the order of x divides the order of f ( x ).