The ranks of classes and nX-complementary generations of the Tits group \(^2F_4(2)′\)

Abstract

Let G be a finite non-abelian simple group. The rank of non-trivial conjugacy class X of G, denoted by rank(G:X), is defined to be the minimal number of elements of X generating G. Also, a group G is said to be nX-complementary generated if given an arbitrary non-identity element x ∈ G then there exists an element y ∈ nX such that G = ⟨x, y⟩. In this paper we establish the ranks of all the conjugacy classes of the Tits group 2F4(2)′ and also classify all the non-trivial conjugacy classes of \(^2F_4(2)′ \) whether they are complementary generators of \(^2F_4(2)′\) or not.