I reproduced the issue in a new Ubuntu Server 16.04 LTS on Azure, as you rightly said the following error appears during the installation
Error: postgres: Error while executing group action
Press [Enter] to continue:
If you press
[Enter] the installation continue without problem and the application is fully installed, note that the installation process may take a while. When the process is finished you can check the installation running this commands (if you choose the default location)
sudo /opt/odoo-10.0.20171015-0/ctlscript.sh status
After that, you should be able to access to your Odoo using the public IP of the server, note that you should configure the Azure Network security group to allow connections in the Apache port (80).
I just noticed we released a new version odoo-10.0.20171118-0 fixing this issue, I edited the first message with the commands to install this new version. Is the one you can find in the Odoo installers page.
Sorry for the confusion.
Carlos R. Hernández