Dear Gap Forum, Is it possible to generate a finite p-group G such that
(1) $G/G_2$ is isomorphic to Z/pZ X Z/pZ (2) $G_2/G_3$ is isomorphic to Z/pZ (3) $G_2$ is of exponent p (4) If g belong to G not $G_2$, then order(g) is bigger than p. Here $G_2$ and $G_3$ are respectively the second and third term in the lower central series. The most natural to think is p-groups of maximal class. But upto order p^p, I think there is no such group. with regards, Siddhartha Sarkar ***************************************************************** Siddhartha Sarkar Research Scholar Dept. of Mathematics Harish Chandra Research Institute Chhatnag Road,Jhusi Allahabad-211019. India. ***************************************************************** _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
