Do you have a nice modern reference where I could find the computation of $H^2(S_n,\mathbb{Z}/2\mathbb{Z})$, where the action is trivial ?

I have looked at the very few books on cohomology of groups I have, but I couldn't find anything. The only reference I know is Schur's original paper, but it is written in German, and the style is quite old-fashioned.

I cannot imagine there is no modern book including this computation...

Thanks in advance for your help.


  • $\begingroup$ This is easily calculated from the Schur Multiplier $H_2(S_n,{\mathbb Z})$ of $S_n$, which has order $2$ when $n \ge 4$. That is proved in Huppert's textbook Endliche gruppen I, but unfortunately that's in German too! $\endgroup$ – Derek Holt Aug 2 '17 at 16:25
  • 1
    $\begingroup$ @DerekHolt Hoffman-Humphreys (1992) does the Schur multiplier in English. $\endgroup$ – Francois Ziegler Aug 2 '17 at 16:47

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