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Aug 28, 2014 at 4:30 comment added Misaka01034 The author of the article define the Heisenberg group to be $(x,a)(x',a')=(x+x',a+a'+\langle x,x'\rangle)$, which differs my definition when $p=2$. But anyway, this definition is still valid and gives a different group.
Aug 26, 2014 at 15:16 comment added Derek Holt Are there different definitions of the Heisenberg group around? The group defined above is not abelian when $q$ is even and $n \ge 1$, and this agrees with the definition on the Wikipedia page, which says that the group is $D_8$ when $n=1$ and $q=2$.
Aug 26, 2014 at 14:26 vote accept Misaka01034
Aug 26, 2014 at 13:53 history edited Dietrich Burde CC BY-SA 3.0
deleted 264 characters in body
Aug 26, 2014 at 13:46 history answered Dietrich Burde CC BY-SA 3.0