A new characterization of L( r) by their Sylow numbers.

Let G be a finite centerless group, let π( G) be the set of prime divisors of the order of G, and let n( G) be the number of Sylow p-subgroups of G, that is, n( G) = |Syl( G)|. Set NS( G):= { n( G)| p ∈ π( G)}. In this paper, we are investigating whether L( r) is determined up to isomorphism by NS( L( r)) when r is prime. [ABSTRACT FROM AUTHOR]