Conjugacy of \(\text{Alt}_5\) and \(\text{SL}(2,5)\) subgroups of \(E_6(\mathbb{C})\), \(F_4(\mathbb{C})\), and a subgroup of \(\mathbb{E}_8(\mathbb{C})\) of type \(A_2E_6\)
Many mathematicians work on solving the embedding and conjugacy problems of finite quasisimple subgroups of exceptional Lie groups. In this paper, the author classifies alternating groups of degree 5 (denoted \(\text{Alt}_5\)) and \(\text{SL}(2,5)\) subgroups of \(E_6(\mathbb{C})\) and \(F_4(\mathbb{C})\) up to conjugacy. The results for \(E_6(\mathbb{C})\) are then used to classify \(\text{Alt}_5\) and \(\text{SL}_2(5)\) subgroups of the centralizer in \(E_8(\mathbb{C})\) of an element of type \(3B\) (a group of type \(A_2E_6\)) which allow to refine the main results in the author's Ph. D. Thesis.
scientific article; zbMATH DE number 1203867
scientific article