## Abstract

In this paper, all spaces are localized at the prime two. Let *T*(1) be the Ravenel spectrum characterized by the *BP*
_{∗}-homology as *BP*
_{∗}[*t*
_{1}], *T*(1)/(*v*
_{1}) be the cofiber of the self map *v*
_{1} : Σ^{2}
*T*(1) → *T*(1) and *L*
_{2} denote the Bousfield localization functor with respect to *v*
_{2}
^{−1}
*BP*
_{∗}. In this paper, we compute the homotopy groups π_{∗}(*L*
_{2}
*T*(1)/(*v*
_{1})) by determining the *E*
_{∞}-term of its Adams-Novikov spectral sequence (ANSS). From the *E*
_{2}-term of the ANSS for π_{∗}(*L*
_{2}
*T*(1)/(*v*
_{1})), we determine a subgroup of the *E*
_{2}-term for π_{∗}(*L*
_{2}
*T*(1)). We also show that the *E*
_{4}-term for π_{∗}(*L*
_{2}
*T*(1)) has horizontal vanishing line.

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