Final answer:
The theological issue over which Pentecostal groups parted company was concerning the Godhead, the Trinity, and the Persons of the Trinity, with debates on the nature and equality within the Trinity.
Step-by-step explanation:
The significant theological issue over which Pentecostal groups parted company is a) The Godhead, the Trinity, and the Persons of the Trinity. The concept of the Trinity has been a cornerstone of Christianity since the second and third centuries. This theological stance posits that God exists simultaneously as three distinct persons: God the Father, God the Son (Jesus Christ), and the Holy Spirit. However, different interpretations and understandings of the Trinity have led to disagreements and separations among Christian groups, including various Pentecostal factions.
One prominent controversy within the Trinity debate centered on the relationship and hierarchy within the Godhead, leading to divergent views such as Arianism, which posited that the persons of the Trinity were not equal. This, along with other divergences in belief concerning the nature and personhood of Jesus and the Holy Spirit, has historically caused rifts and the formation of new denominations or sects within the Christian faith. It remains a topic that both unites and divides Christian communities to this day.