[GAP Forum] Image homomorphism(Tensor sqaure)

[Ellis, Grahamj]

The HAP function
 
Trec:=NonabelianTensorSquare(G);
 
returns a record with
 
T:=Trec.group;
 
the tensor square of G, and
 
h:=Trec.pairing;
 
the crossed pairing h(x,y):GxG --> T.
 
This crossed pairing could be used to obtain the image of your homomorphism below. (Though I guess the exact sequence should be
 
(K \otimes G) x (G\otimes K) ---> G \otimes G ---> (G/K)\otimes (G/K) ---> 1
 
if K is central in G.  )
 
Graham


School of Mathematics, Statistics and Applied Mathematics 
National University of Ireland, Galway
http://hamilton.nuigalway.ie

________________________________

From: forum-bounces at gap-system.org on behalf of Takjk Taj
Sent: Sat 17/01/2009 14:51
To: forum at gap-system.org
Subject: [GAP Forum] Image homomorphism(Tensor sqaure)



Dear GAP forum,
Brown and Johnson Robertson proved in [*]
for given a central extension
1 --> K ---> G ----> G/K ---->1
there is an exact sequence
(A\otimesK)x(K\otimes A) \Stackrel {l} ------> K\otimesK ---> G\otimes G ---> 1
in which Im(I) is central.
Can we calculate Im (l)  with GAP?
every suggestion is welcome.
Thanks
*. Some Computations of Non-Abelian Tensor
Products of Groups, JOURNAL OF ALGEBRA 111, 177-202 (1987).



     
_______________________________________________
Forum mailing list
Forum at mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum