GPL and server appliances

[Jerome Alet]

Hi there,

one idea came to my mind (not exactly from nowhere, but this doesn't 
matter for now) 

say you write some piece of software and publish it under the GNU
GPL license.

say some company (A) enhances your software, install the new 
combined product on a server appliance, and put the server appliance 
at a third party company (B, its client), but DOESN'T SELL the 
server appliance to B. Instead of selling it, A is still the full 
owner of server appliance, which is installed at B's location only 
as part of a support contract. 

A DOESN'T WANT TO deliver full source code of the combined product 
to B under the terms of the GNU GPL. 

Question : does company A violate the GPL or not by not distributing 
full source code under the terms of the GPL to B ?

(Of course I understand that A is not required to distribute full 
source code to the general public or even to you as principal author 
of the original software) 

Thanks in advance for any clarification

Jerome Alet