COMMUTATOR IDENTITIES OBTAINED BY THE MAGNUS ALGEBRA

I. Introduction. In this paper, two related commutator identities are established through the use of the Magnus Algebra (the algebra of noncommutative formal power series with integral coefficients). These identities are connected with identities of P. Hall (Theorem 12.3.1 of [1] and Theorem 3.1 and 3.2 of [2])and ofR. R. Struik (equation (56) of [4] and Theorem 1 of [5]). They involve basic commutators. Th