Finite simple groups of Lie type have non-principal p-blocks, p\(\neq 2\)
The paper gives a proof of the titular theorem. After the introduction, section 2 gives the prerequisites from block theory. Section 3 summarizes known results on maximal tori and the structure of semisimple elements of finite groups G of Lie type. In section 4, the proof proceeds by destroying the minimal counterexample L; here \(L\cong G/Z(G)\). By case by case analysis, it is shown that every p-element x in \(G\setminus Z(G)\) is regular, using the centralizer \(C_ G(x)\) of semisimple x; further \(p\nmid | Z(G)|\). The argument concludes by using a theorem of Boyce to show that a Sylow p-subgroup S of G must be cyclic and in this case a theorem of the second author implies that L must have at least two blocks, the final contradiction.
scientific article; zbMATH DE number 3983455
scientific article