A problem with the proof of a proposition I have a problem with the proof of Proposition 5.1. of the article of Ito.(Noboru Itˆo. On finite groups with given conjugate types. I.
Nagoya Math. J., 6:17–28, 1953.).
I don't know what is "e" and "e-1" in the proof.
I'd be really greatfull if someone help me.You can find the pdf file in this link.
Link

I would appear that $e$ is a group. Whenever the author writes $e-1$ they actually have "some group":$e-1$, so they just mean the index of $e$ in the group, minus one.
As to what $e$ is I am not sure, but I would guess it is related to $E$. I am not even sure whether $E$ is a group or an element, but most of the time it appears to be an element, and I would guess that $e$ is the group generated by $E$.
Edit: As Derek Holt has commented below, $e$ is probably the trivial group, and hence $[G:e]$ is just the order of $G$.
