No abstract

No abstract

A subgroup H of a group G is c-subnormal in G if G has a subnormal subgroup T such that HT=G and T 3 H ⊆ HG.^[1] Using this concept, in Jaraden obtain^[1] some new conditions for solubility of a finite group are given. Here we obtain local versions of these results

Let G be a finite group. We say that a subgroup H of G is [Formula: see text]-normal in G if G has a subnormal subgroup T such that TH = G and (H ∩ T)HG/HG is contained in the [Formula: see text]-hypercenter [Formula: see text] of G/HG, where [Formula: see text] is the class of the finite supersoluble groups. We study the structure of G under the assumption that some subgroups of G are [Formula: see text]-normal in G.

No abstract