The maximal abelian extension contained in a division field of an elliptic curve over Q with complex multiplication

Let K be an imaginary quadratic field, and let O₊, ₅ be an order in K of conductor f 1. Let E be an elliptic curve with CM by O₊, ₅, such that E is defined by a model over Q (j₊, ₅), where j₊, ₅=j (E). It has been shown by the author and Lozano-Robledo that Gal (Q (j₊, ₅, EN) /Q (j₊, ₅) ) is only abelian for N=2, 3, and 4. Let p be a prime and let n 1 be an integer. In this article, we bound the commutator subgroups of Gal (Q (Epⁿ) /Q) and classify the maximal abelian extensions contained in Q (Epⁿ) /Q.