7.53 (1980)

Let $p$ be a prime. The law $x \cdot x^\varphi \dots x^{\varphi^{p-1}} = 1$ from the definition of a splitting automorphism (see 1.10) gives rise to a variety of groups with operators $\langle \varphi \rangle$ consisting of all groups that admit a splitting automorphism of order $p$. Does the analogue of Kostrikin’s theorem hold for this variety, that is, do the locally nilpotent groups in this variety form a subvariety?