  Let M(1) be the mod 2 Moore spectrum. J.F. Adams proved that M(1) admits a
minimal v_1-self map v_1^4: Sigma^8 M(1) -> M(1). Let M(1,4) be the cofiber of
this self-map. The purpose of this paper is to prove that M(1,4) admits a
minimal v_2-self map of the form v_2^32: Sigma^192 M(1,4) -> M(1,4). The
existence of this map implies the existence of many 192-periodic families of
elements in the stable homotopy groups of spheres.
