Can pokemon of the same egg group learn the same type of moves?

this is the entire question because since arbok is in the dragon group i might think that it could've learnt some dragon move such as dragon pulse from gible from wayward cave at least but i am asking other experts to give me a real answer but i am going on my hunch that you can probably teach them dragon moves or else why would arbok be in that group you could just put it on some other random group which is more compatible with it's own type