Isn't the quaternion group an example?
Steve
On Sat, 15 Oct 2005 14:09:08 +0530 (IST)
Siddhartha Sarkar <[EMAIL PROTECTED]> wrote:
>
> 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.
> *****************************************************************
>
>
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--
Steve Linton School of Computer Science &
Centre for Interdisciplinary Research in Computational Algebra
University of St Andrews Tel +44 (1334) 463269
http://www.dcs.st-and.ac.uk/~sal Fax +44 (1334) 463278
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