Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

A NEW CHARACTERIZATION OF ALTERNATING AND SYMMETRIC GROUPS

  • ALAVI S. H. (Department Mathematics, Bu-Ali Sina University) ;
  • DANESHKHAW A. (Department Mathematics, Bu-Ali Sina University)
  • Published : 2005.01.01

⟨ Previous Next ⟩

Abstract

In this paper we prove that the alternating groups A_n, for n = p, p+1, p+2 and symmetric groups $S_n$, for n = p, p+1, where p$\ge$3 is a prime number, can be uniquely determined by their order components. As one of the important consequence of this characterization we show that the simple groups An, where n = p, p+1, P+2 and p$\ge$3 is prime, satisfy in Thompson's conjecture and Shi's conjecture.

Keywords