Timeline for p-group with large center

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Feb 25, 2013 at 17:39	history	edited	Arturo Magidin	CC BY-SA 3.0	add details in light of comment
Feb 25, 2013 at 15:30	comment	added	Arturo Magidin		@Johannes Hahn: The map has image which generates $[G,G]$; since the bilinear form is alternating, in the case at hand the image is generated by $[x,y]$ (where $G/Z(G)$ is generated by the images of$x$ and $y$), hence $[G,G]$ is cyclic; and since the map is bilinear, it will perforce be onto in this situation (rather than merely mapping onto a generating set). Since $G/Z(G)$ is of exponent $p$, $[x,y]$ is of order $p$, and so $[G,G]$ is cyclic of order $p$.
Feb 25, 2013 at 14:48	comment	added	Johannes Hahn		Wait a minute... what map from $G/Z(G)\times G/Z(G)$ onto $[G,G]$ are you talking about? The commutator? That isn't onto in general. Also why should $[G,G]$ be cyclic of order $p$? Could you please eloborate on that? Thanks.
Feb 25, 2013 at 4:39	history	answered	Arturo Magidin	CC BY-SA 3.0