More about quark Yukawa textures from selection rules without group actions

A bstract We study the coupling selection rules associated with non-group symmetries, i.e., ℤ 2 gauging of ℤ M symmetries. We clarify which Yukawa textures can be derived by our selection rules for M = 3 , 4, and 5, and obtain various textures including the nearest neighbor interaction type and its extension. Some of them cannot be realized by a conventional group-like symmetry. They lead to interesting phenomenology such as a solution to the strong CP problem without axion.