2018/05/14 by Zhenfeng Wu, Chi Zhang, Wu, Zhenfeng +3
Mathematics · #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.1805.05097
Let σ=\σi|i∈ I\ be some partition of the set ℙ of all primes, that is, ℙ=\bigcupi∈ Iσi and σi∩ σj=∅ for all i≠ j. Let G be a finite group. A set \mathcal H of subgroups of G is said to be a complete Hall σ-set of G if every non-identity member of \mathcal H is a Hall σi-subgroup of G and \mathcal H contains exactly one Hall σi-subgroup of G for every σi∈ σ(G). G is said to be a σ-group if it possesses a complete Hall σ-set. A σ-group G is said to be σ-dispersive provided G has a normal series 1 = G1