This question may seem elementary to experts but I am quite confused about it:

According to the entry of Lyndon–Hochschild–Serre spectral sequence on wikipedia, for a group extension $1\to N\to G\to Q\to1$, there is a Lyndon–Hochschild–Serre spectral sequence if $G$ is a profinite group and $N$ is a closed normal subgroup of $G$:

http://en.wikipedia.org/wiki/Lyndon-Hochschild-Serre_spectral_sequence

Also in the book Neukirch, Jürgen; Schmidt, Alexander; Wingberg, Kay (2000), *Cohomology of Number Fields*, the same condition was assumed.

However, according to some other books, for example Brown, Kenneth S. (1972), *Cohomology of Groups*, and *A User's Guide to Spectral Sequences* by John McCleary, the profiniteness condition on the group $G$ was NOT assumed.

Why there is such a difference? Do we really need the condition that $G$ is a profinite group and $N$ is a closed normal subgroup of $G$ to construct the Lyndon–Hochschild–Serre spectral sequence?

continuousmaps $G^{n+1} \to A$ while for abstract groups you useallmaps $G^{n+1} \to A$. //And, of course, I agree with Mark that a-fortiori should make his/her comment into an an answer. – Ralph Apr 27 '12 at 9:50