[iScience]

in class, i learned that the open valence ended propane was called the 'n-propyl' group, and same for open valence ended butane groups, we learned these to be the 'n-butyl' group, but on this page
http://www.cem.msu.edu/~reusch/OrgPage/bndenrgy.htm

there is i-propyl and t-butyl. what do the different letters represent? are they arbitrary?

[discodermolide]

The letters are not arbitrary. They stand iso and tertiary and represent isomers of the parent compound.
So you have propanol, a straight chain and iso-propanol where you now have the OH being attached to the middle carbon like this:

and iso

See if you can draw all the isomers for butanol.