Not sure what you mean with the child window. But I think window.opener may be what you are looking for.
// Call abc in the window that opened the current window window.opener.abc();
Update
I have not tried it, but since window.opener is a link to a window that opens the current window, I think you should be able to call the opener property in this link to get a link to its parent:
window.opener.opener.abc();
If you want to get to the topmost window (the root window or what you would call it), you can use window.top instead:
window.top.abc();
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