Nomenclature - IUPAC and Common Names

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What if we stuck with the IUPAC name and called the isopropyl group a 1-methylethyl group? That would definitely reverse the alphabetical priorities; because the substituents here on the hydrocarbon are on equivalent positions, we must give the lower number to the substituent that comes first in the alphabet.

But that's the rub! (No isopropyl alcohol pun!)

Isopropyl - "I" comes before "M" as in methyl.

But if we name the isopropyl group systematically,

Methylethyl comes after just methyl in the alphabet.

So could the name of this also be:

1,1-dimethyl-7-(1-methylethyl)bicyclo[3.2.0]heptane?
 
on Phys.org
The numbers, in this case, are unambiguous.The largest ring is numbered lowest.
but you seem to be confusing two different things, the numbering of the carbons (atoms) and the ordering (alphabetical) of the name.
2-propyl is NOT systematically methylethyl.
It is 7,7-dimethyl-2-(2-propyl)bicyclo[3.2.0]hepatane, (imho).
But nobody will be confused by 7,7-dimethyl-2-(isopropyl)bicyclo[3.2.0]hepatane
but I think *might be* by 7,7-dimethyl-2-(methylethyl)bicyclo[3.2.0]hepatane (did you mean 2-methyl-2-ethyl?)
imho, iso, just like di, tri, etc. prefixes, should be ignored in alphabetization. (sec, tert, neo, ...)
Been years since I worried about this stuff. Truth is, few Chemists can be trusted to be 100%, so you got to be flexible when searching (that is, aliases abound). So, while you can worry about which is "the" right name, that won't stop anybody else from doing their own thing.