I'm not sure how the wheel group is treated in docker-alpine but why does it exist if one can gain root privileges without being member of it?
# docker run -i -t --name="test" alpine /bin/sh
/ # adduser -S testuser
/ # groups testuser
nogroup
# docker exec -it --user=testuser test /bin/sh
/ $ whoami
testuser
/ $ su
/ # whoami
root
/ # groups testuser
nogroup
/ # groups root
root bin daemon sys adm disk wheel floppy dialout tape video
/ #
In ubuntu-docker this does not work.