As title, I'm doing a problem in algeraic topology, and met this group, I need to figure out what it is. I met similar group such as $\langle a,b,c\mid c=1\rangle $ and $\langle a,b,c,d\mid cd=1\rangle$, I believe these two are both free groups, but not sure what happens when adding another generator.
2026-03-27 10:09:06.1774606146
what is the group $\langle a,b,c,d,e\mid cde=1\rangle$?
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As already pointed out by ahulpke, all you can say is that your group is a free group in 4 generators say $a,b,c,d$ and the fifth element namely $e$ can be written as a word in the form : $e=d^{-1}c^{-1}$ . In this case drawing a Cayley graph is easy: