19.13 (2018)

The well-known Baer–Suzuki theorem states that if every two conjugates of an element $a$ of a finite group $G$ generate a finite $p$-subgroup, then $a$ is contained in a normal $p$-subgroup. Does such a theorem hold in the class of periodic groups for $p > 2$? A counterexample is known for $p = 2$; see 11.11 a).