Good contributors to the order of the finite simple groups
Let G be a nonabelian simple group of order \(| G| =p_ 1^{n_ 1}\cdot p_ 2^{n_ 2}\cdot...\cdot p_ s^{n_ s}\) with \(p_ 1^{n_ 1}>p_ 2^{n_ 2}>..>p_ s^{n_ s}\) and \(p_ 1,p_ 2,...,p_ s\) distinct primes. We call \(p_ i\) a good contributor to \(| G|\) if \((p_ i^{n_ i})^{\log 3/\log 2}\geq p_ 1^{n_ 1}.\) We obtain an explicit description of the good contributors of all finite simple groups with the exception of the groups \(PSL_ 2(q)\), \(PSU_ 3(q)\), \(PSL_ 3(q)\).
scientific article; zbMATH DE number 3871622