A conjecture of Frobenius and the simple groups of Lie type. IV
Let \(G\) be a finite group, \(e\) be a positive integer dividing \(| G|\) and \(L_ e(G) = \{x \in G \mid x^ e = 1\}\). Frobenius showed that \(| L_ e(G)| \equiv 0 \pmod e\) and conjectured that \(L_ e(G)\) forms a subgroup provided \(e = | L_ e(G)|\). This paper is one in the series of articles which proves the Frobenius conjecture modulo the classification of the finite simple groups [for part III, cf. the author and \textit{H. Yamaki}, ibid. 145, No. 2, 329-332 (1992; Zbl 0745.20014)]. Indeed, the author proves that the Frobenius conjecture is true for the simple groups \(B_ n(q)\), \(D_ n(q)\), \(^ 2 A_ n(q)\) and \(^ 2 D_ n(q)\).
classification of the finite simple groups
scientific article; zbMATH DE number 130516