Dear Graham, Dear Forum,

> Is there a way to construct a group homomorphism using a variant of the 
> function
> 
> f:=GroupHomomorphismByFunction(G,H,x->function(x))
> 
> for which
> 
> ImageElm(f,x)
> 
> does not test to see if x lies in G?  Here function(x) is a well-defined 
> function for x in G, but G is a group for which I don't have a membership 
> test.

In such situations (e.g. with matrix groups, using the `matgrp` package), I use 
`ImagesRepresentative` in place of `Image` or `ImageElm` to avoid membership 
test.

All the best,

   Alexander



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