Hi,
User is a member of AD "linux_admin" group. When I run 'id', it
doesn't show he is member.
By sudo log, do you mean sudo debug log ? I have following there:
sudo[1069] sudo_getgrnam: group linux_admin [] -> gid 10001 [] (cached)
sudo[1069] sudo_get_gidlist: looking up group IDs for testadmin
sudo[1069] user_in_group: user testadmin NOT in group linux_admin