• A NOTE ON WEISENER THEOREM1

Abstract

Let π(n) be the prime divisor set of n and called that n is a π(n)-number. Denote by nπ the greatest divisor of n whose prime divisor set is π. Let G be a finite group. Weisener Theorem states that the number w(n) of elements whose orders are multiples of n is either zero, or a multiple of |G|π(|G|)\π(n). In this paper we classify groups satisfied w(n) is 0 or a π(|G|)\π(n) -number.

Keywords: Weisener theorem, number of elements, finite groups.

MR (2000): 20D60, 20D06.