Affiliation:
1. Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
2. Department of Mathematics, Francisk Skorina Gomel State University, Gomel 246019, Belarus
Abstract
For each finite group E, let Θ(E) be a binary relation on the set of all subgroups of E. If A and B are subgroups of a finite group G, then we say that the pair (A, B) enjoys the gradewise property (resp., generalized gradewise property) Θ in G if G has a normal series Γ : 1 = G0 [Formula: see text] such that for each [Formula: see text], we have [Formula: see text] (resp., we have [Formula: see text]. Using these concepts, we obtain some new characterizations for solubility and supersolubility of finite groups and generalize some known results.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory