I have been asked to post my private response to the Forum. This has made no use at all of GAP. It would be interesting to know how someone who can't drag examples from thier personal archive might use GAP to find some.
Mike Newman Message from erfanian <[EMAIL PROTECTED]> ----- Dear All, I am looking for an example of a group $G$ with the property that $G/Z(G)$ is a p-elementary abelian of rank $k\geq 3$ and for every elements $x \in G\Z(G)$ we have $[G : C_G(x)}=p$. I will be more grateful for any comments. Response: The extra-special groups are examples. These are groups with class 2 whose centre and commutator subgroup coincide and have order p. The finite extra-special groups are central products of the non-abelian groups with order p^3. The central product of an extra-special group and an abelian group is also an example. These are the only finite examples. _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
