On the number of conjugacy classes of maximal subgroups in a finite soluble group
Archiv der Mathematik
1 - 8
Item Usage Stats
MetadataShow full item record
We show that for many formations U-fraktur sign, there exists an integer n = m̄(U-fraktur sign) such that every finite soluble group G not belonging to the class U-fraktur sign has at most n conjugacy classes of maximal subgroups belonging to the class U-fraktur sign. If U-fraktur sign is a local formation with formation function f, we bound m̄(U-fraktur sign) in terms of the m̄(f(p)) (p ∈ ℙ). In particular, we show that m̄(ℜk) = k + 1 for every nonnegative integer k, where ℜk is the class of all finite groups of Fitting length ≦ k.