We can use the usermod command to add a user to a group. Here I am going to add the user grokman to the group adm:
root@myserver:~# sudo usermod -aG adm grokman
root@myserver:~# exit Connection to myserver closed.
root@myserver:~# ssh myserver Welcome to ...
root@myserver:~# groups admin adm sudo www-data
In Debian / Ubuntu, the being in the adm group will allow you to view logs & do general system monitoring.
Tested on Ubuntu 18.04.5