what kind of radioactive decay does not cause transmutation

 Transmutation is when an a nucleus changes from one atom to another.

gamma decay is the e type of radioactive emission that does not cause any transmutations, in a gamma decay,  the nucleus is in the excited state and only emits energy to return to ground or unexcited state, ,

 secondly gamma ray does contain any nuclear particle therefore its emission does not change the number of nucleons in the atom. In other words the emission of gamma ray does not change the atomic number or atomic mass of  the parent nucleus and therefore after gamma decay, the parent nucleus an daughter nucleus are the same

 Example of gamma  emission are

⁶⁰₂₈Ni^* →⁶⁰₂₈Ni +    + 1.33 MeV

 here the parent and the daughter nucleus are the same therefore no trans mutation has occurred.