It is often overlooked that Italy were allies with Nazi Germany in WW2. I actually until recently totally forgot this was the case. I was never taught anything on the subject matter about Italy at that time except that my grandfather was a PoW in Italy until he escaped.
Hope this is acceptable to the admins but this is a link to a published copy of his memoires of his time as a soldier.
Were the Italian government complicit with the Nazi party, how much did they know about the atrocities towards the Jewish population? Did they share the same racial purity beliefs of their German allies?
Mussolini and Hitler had a rocky relationship to start with. After the Veince conference where they had their first real discussion, both men had lower opinions of each other. Hitler still admired and looked up to Mussolini as a role model and because of the role Mussolini had played in founding fascism. Mussolini on the other hand really disliked Hitler. He criticized mein Kampf as stupid book, he claimed that Hitler's ideas were simplistic, and that the idea of racial purity or a master race were foolish. Mussolini wasn't a progressive or anything, and he like many people at the time considered the white race to be superior; but he wasn't as radical as Hitler.
Now as for the Jewish question. Mussolini's government originally paid them no mind. And during the holocaust they steadfastly refused to give up their Jewish population to the Germans. Now eventually Mussolini caved and enacted anti Jewish laws like the ones in Germany, but still didn't start a mass killing program or anything. However, after the Italian collapse the German puppet state the Italian Social Republic headed by Mussolini was complicit in the holocaust and did give up their Jews.
If you want more about Mussolini and his relationship with Hitler read "Mussolini" by Dennis Mack Smith.