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The full name is Oracle Enterprise Manager Console. You can download the 10g version from here. You can find a user/pass on bugmenot. After unzipping, just running '/path/toclient/runInstaller -ignoreSysPrereqs' (I only tried with an absolute path) should be enough. It can be installed a user, later it'll prepare some scripts to run as root.
I always replaced $HOME/orafoo with $HOME/.orafoo, when the installer asked. If you get 'no such file or directory' errors, you can just edit the relevant script and fix the path - I needed to fix /bin/rpm, /bin/awk and /bin/sed. (All of them are under /usr/bin.) A hack for the lazy ones: just symlink these to /bin, then no modification of the scripts is needed.
To your ~/.bash_login:
export LIBXCB_ALLOW_SLOPPY_LOCK=true export ORACLE_HOME=~/.oracle/product/10.2.0/client_1/