TITLE: Why are Thompson's groups called $F$, $T$ and $V$?
QUESTION [17 upvotes]: Why are Thompson's groups called $F$, $T$ and $V$?

I never saw Thompson's unpublished notes, in which he introduces these groups; maybe an explanation can be found there?

REPLY [5 votes]: Matt Zaremsky's justification of "$F$" for "free" can also be found in Ross Geoghegan's review MR1239554 on Mathscinet.
I also took a look at McKenzie and Thompson's article An elementary construction of unsolvable word problems in group theory (MSN) (which seems to be the first publication mentioning the groups constructed by Thompson), and there is some history in §8. Below is a screenshot:

The groups $\mathfrak{P}$ and $\mathfrak{P}'$ correspond to the group now called $F$. From the context, $\mathfrak{P}$ probably refers to the "p" of "permutation". The group $\mathfrak{C}'$ corresponds to the group now called $V$. I would guess that $\mathfrak{C}$ refers to the "C" of "Cantor space".