Don't add Cedric to group
jack, because that is Jack's personal group. It's a security violation.
In addition to that, in new versions of Ubuntu, the default access to home accounts and files will be 600 for files and 700 for folders, i.e. groups and others can't access the area at all. This is recommended for security, because in previous versions, anyone could access (but not modify) anyone else's data.
You can explicitly set this in older versions of Ubuntu for all of the various home folders as follows:
sudo chmod --recursive go= /home/
A side effect of this is that no matter how you set your secret file within Jack's folder, no one can access it. That's a Good Thing (as Winnie the Pooh might say), both for security and because Jack's folder is personal to Jack.
The right way is to create a brand new folder, not in Jack's area, that all permitted people, and only permitted people, can share.
You specify who may share with a new common group created just for the purpose. You assign the file's ownership to Jack, who can write to the file, and the file's group to the new common group, whose members can read but not modify the file.
Here are the steps. For this example, I've used the folder
/home/secshare and the group name
secacc, but you can choose a different name for both the folder and the group name (they can have the same name as each other, if you like).
sudo groupadd secacc # Create the new security group.
sudo mkdir /home/secshare/ # The folder to hold the security file.
sudo chown jack:secacc /home/secshare/ # Jack owns the folder. Group has access.
sudo chmod u=rwx,g=rx,o= /home/secshare/ # Jack: rw. Group: r. Others: none.
# Create the file.
echo secret5cd51b | sudo tee /home/secshare/secret7b079
sudo chmod g=r,o= /home/secshare/secret7b079 # Owner: rw. Group: r. Others: none.
# Assign Jack as the owner, and secacc as the group.
sudo chown jack:secacc /home/secshare/secret7b079
# Double-check permissions.
sudo ls -l --directory /home/secshare/
> drwxr-x--- 2 jack secacc 4096 Feb 8 11:48 /home/secshare/
sudo ls -l /home/secshare/
> -rw-r----- 1 jack secacc 13 Feb 8 11:48 secret7b079
# Assign both Jack and Cedric to the group secacc
sudo usermod --append --groups secacc jack
sudo usermod --append --groups secacc cedric
At this point, Jack has full access to both the folder and the files within.
Cedric belongs to group
secacc and therefore has read-only access to both the folder and the files within.
Pedri, who doesn't belong to the group
secacc, has no access to the folder, and no access to the files within (even if the files within have full read-write access to everyone — test it for yourself).