Characterization of finite groups by a bijection with a divisible property on the element orders. Issue 8 (3rd August 2017)

• Record Type: Journal Article
• Authors: Jafarian Amiri, Seyyed Majid; Amiri, Mohsen
• Is Part Of: Communications in algebra. Volume 45:Issue 8(2017)
• Page Start: 3396
• Page End: 3401
• Publication Date: 2017-08-03
• Subjects: Bijection -- finite group -- order element -- quaternion group; 20D60; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1236932
• Languages: English
• ISSNs: 0092-7872

Abstract

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 ).