[GAP Forum] a question about p-groups

[Steve Linton]

Isn't the quaternion group an example?

	Steve

On Sat, 15 Oct 2005 14:09:08 +0530 (IST)
Siddhartha Sarkar <sidhu at mri.ernet.in> 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
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