Graded antisimple radicals (Q1125598)

Let \(G\) be an arbitrary group. The aim of this paper is to introduce and investigate the graded antisimple radical \(\mathbb{S}_G\), which is the graded version of the antisimple radical \(\mathbb{S}\). It is shown that in case the group \(G\) is finite, the graded antisimple radical \(\mathbb{S}_G\) is equal to the graded reflected radical \(\mathbb{S}_{\text{ref}}\) and to the graded restricted radical \(\mathbb{S}^G\).