Dear Gap-Forum,
The GAP3.4.4 (DOS) code below gives a strange result: the semidirect
product's size differs before and after printing its elements. If printing
is omitted, the sizes agree (12).What causes this? Thankx.
Bruce
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G := SymmetricGroup(3);
f := IdentityMapping(G);
N := CyclicGroup(2);
sdp := SemidirectProduct(G,f,N);
Print("Size1 ",Size(sdp));
[...]
The problem here seems to be that the function SemidirectProduct
apparently gets confused...
(indeed, the input data doesn't really make sense here)
Nevertheless, the behavour is amusing (same under UNIX): indeed: gap> G := SymmetricGroup(3); Group( (1,3), (2,3) ) gap> N := CyclicGroup(2); Group( (1,2) ) gap> f := IdentityMapping(G); IdentityMapping( Group( (1,3), (2,3) ) ) gap> Size(SemidirectProduct(G,f,N)); 12 gap> Length(Elements(SemidirectProduct(G,f,N))); 36 gap> Size(Elements(SemidirectProduct(G,f,N))); 36 gap>
Probably it's a bug rather than a feature :-)
Regards,
d.pasechnik@twi.tudelft.nl