There are at least four bands called Abnormity.
By chronological order they are:
1) Russian Slamming Brutal Death Metal band who released their debut album "Irreversible Disintegration" in 2011.
2) Swedish Death Metal band formed in 1990 which released their only demo in 1991.
3) Italian Death Metal band which released a demo in 1998.
4) Spanish Death/Doom Metal band which formed in 1999 and released their only demo in 2002.
5) German Thrash Metal band formed in 2002 which released a self-titled demo in 2006 and a full length in 2008, called Come Get Some. The band is still active.