After the great schism of 1054, when the east and west roman empires split religious beliefs, what two main groups were the result?

The Roman Catholic and the Eastern Orthodox faith.

The Great Schism of 1054 was a religious conflict between the western and eastern branches of the church. There were several issues that divided the church's opinion, such as the use of unleavened bread, the role of the Holy Ghost, and more importantly, the authority of the Bishop of Rome (the Pope). On July 16, 1054, the Patriarch of Constantinople Michael Cerularius was excommunicated, effectively leading to the schism.

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