Title: On the orders of the non-Frattini elements of a finite group,
Abstract: Let $G$ be a finite group and let $p_1,\dots,p_n$ be distinct primes. If $G$
contains an element of order $p_1\cdots p_n,$ then there is an element in $G$
which is not contained in the Frattini subgroup of $G$ and whose order is
divisible by $p_1\cdots p_n.$