One silly chmod question

[ESGLinux]

Hi all,

I have a problem changing permissions to some files using chmod and now I
have a doubt about the owner and group of a file,

I´ll try to explain.

I have 2 users, user1 and user2, both belongs to group1.

I have a file with this permissions:
-rwxrwxrwx 1 user1 group1 file.txt

with user2 I can read, write this file. but If I try to change the
permissions with this:
chmod 770 file.txt I get the error:
operation not permitted,

so my doubt is, only the owner can change the permissions to a file?

Thanks,

ESG