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Mar 19, 2013 at 4:50 vote accept Marius Tarnauceanu
Mar 18, 2013 at 11:31 history edited Amritanshu Prasad CC BY-SA 3.0
Deleted claim that the problem easily reduces to odd order groups.
Mar 18, 2013 at 11:00 comment added Amritanshu Prasad The reduction-to-matrix-groups over $\mathbf Z/p\mathbf Z$ idea works for $2$-groups as well; so you need to figure out when an invertible matrix in $\mathbf Z/2\mathbf Z$ is a sum of two invertible matrices. Tom Goodwillie suggests that this holds for matrices that are at least $2\times 2$.
Mar 18, 2013 at 6:34 comment added Marius Tarnauceanu Thank you very much. The real problem is for finite abelian 2-groups.
Mar 16, 2013 at 13:53 history edited Amritanshu Prasad CC BY-SA 3.0
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Mar 16, 2013 at 11:27 history edited Amritanshu Prasad CC BY-SA 3.0
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Mar 16, 2013 at 11:20 history answered Amritanshu Prasad CC BY-SA 3.0