Cyclic TI-subgroups of order \(4\) in classical Chevalley groups of odd characteristic (Q5918036)

A subgroup \(A\) of \(G\) is called a TI-subgroup if \(A\cap A^g=1\) for every \(g\in G\setminus N_G(A)\). The article under review deals with the groups \(G\) such that \(F^*(G)\) is a classical group of Lie type over a field of odd characteristic and \(G=F^*(G)A\), where \(A\) is a cyclic TI-subgroup of order 4 in \(G\) and \(A\not\subseteq Z(F^*(G))\). In this case, all the possibilities for \(F^*(G)\) and \(A\) are described.