On $TI$-subgroups of finite groups

The author studies the normal closure in a finite group of an elementary $2$-subgroup $A$ which is a $TI$-subgroup, and which satisfies the following condition: for an arbitrary collection $A_1,A_2,\dots,A_k$ ($k\geqslant2$) of distinct commuting subgroups conjugate to $A$, the product $A_2\dots A_k$ does not contain $A_1$.
Bibliography: 17 titles.