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Mar 2, 2013 at 12:50 vote accept Yassine Guerboussa
Mar 2, 2013 at 12:39 comment added Yassine Guerboussa I am grateful, Prof. Derek Holt, excuse me to add ( of course in the light of your example): we can replace <x,y> in your example by any elemantary abelian p-group E, we choose an arbitrary non-trivial action of v on E, and we extend it to E+<w> by setting [v,w]=w^p and [v,w^p]=1. So we can obtain counter examples of arbitrary large order.
Mar 2, 2013 at 10:48 history answered Derek Holt CC BY-SA 3.0