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Aug 7, 2014 at 9:32 comment added Anurag But I suppose those groups are too special and this result won't be true in general.
Aug 7, 2014 at 9:19 comment added Anurag Interesting. I wonder how I missed that when I was checking this for alternating groups. So, clearly commutativity is not enough to deduce that product of two central involutions is also central. Can you think so some other conditions that will suffice? Some famous examples of groups where this sort of closure is true and used are $J_2$ and $Suz$.
Aug 7, 2014 at 9:08 history answered Derek Holt CC BY-SA 3.0