In the paper we consider some commutator-type and power-type matrix equations in the group UT(∞,K) of infinite dimensional unitriangular matrices over a fieldK. We introduce a notion of a power outer commutator ω1k k (x1, ..., xk) and a power Engel commutator e1k k (x, y) as outer (respectively Engel) commutators modified by allowing powers of letters instead of letters alone. For a given infin...

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