[GAP Forum] Constructing a 2-Engel group

[Alireza Abdollahi]

Dears,
How one can try by GAP to construct a group G with the
following properties:
 
A finite 2-Engel 3-group G such that
|G|=3^{11},
G^3=G'=C_9 X C_9 X C_9 X C_3,
Z_2(G)=C_9 X C_9 X C_9 X C_9,
 \Omega_1(G)=Z(G) \cap G'=(Z_2(G))^3 and exp(G)=27,
where \Omega_1(G) is the subgroup of G generated by
all  elements x in G such that x^3=1.

Thanks in advance for any help.


Best Regards

A. Abdollahi






--- saf at sci.ui.ac.ir wrote:

> Date: Sat, 12 Nov 2005 10:48:16 +0330
> From: saf at sci.ui.ac.ir
> To: "a.abdollahi" <a.abdollahi at math.ui.ac.ir>,
>         abdollahi <abdollahi at member.ams.org>,
> aabdolla <aabdolla at ictp.it>,
>         "a.abdollahi" <a.abdollahi at sci.ui.ac.ir>
> Subject: a 2-Engel group
> 
> 
> 
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> \opening{Dear Dr.Abdollahi,}
> 
> Does there exist a 2-Engel group $G$ such that
> $|G|=3^{11}$,
> \\$G^3=G^{'}=C_9 \times C_9 \times C_9 \times C_3,
> Z_2(G)=C_9\times C_9 \times
> C_9 \times C_9,$
> \\$ \Omega_1(G)=Z(G)\cap G^{'}=(Z_2(G))^3$ and
> $exp(G)=27$.
> 
> 
> \closing{Sincerely yours,}
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Alireza Abdollahi
Department of Mathematics
University of Isfahan, 
Isfahan 81746-73441,Iran
e-mail: abdollahi at member.ams.org
        a.abdollahi at math.ui.ac.ir
URL:    http://sci.ui.ac.ir/math/New/abdollahi.htm


	
		
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