did she controll directly rome for four years??
I'm not sure. Here is some more info from 'Papal genealogy, the families and descendants of the popes' by George L. Williams (pp. 13-14):
Marozia
Born around 890, Marozia had married as her first husband the Duke of Spoleto, Alberico I. In her youth she had taken a lover, purportedly Pope Sergius III, and a son had been born of this unionaround 906. As mentioned earlier, the relationship between Marozia and Sergius is recorded by Liutprand, but it has been disputed. It is not known when Marozia married Alberico I, and her relationship with Sergius, encouraged by her parents, may have been adulterous. Four children were born of her marriage to Alberico: Duke Alberico II, Sergius (later bishop of Nepi), Constantine and a daughter. While her parents and husband were alive, her power in Rome was assured; but upon their deaths, Marozia felt threatened by Pope John X. (Liutprand also accused Marozia of having "illicit intercourse" with this pope as well.) The pope, in turn, wanted to free himself from the influence of the Roman aristocracy, especially the family of Teofilatto. After all, it was Teofilatto and Teodora who not only had nominated the popes, but who had ruled the government. In an attempt to assert his independence, Pope John X formed an alliance with Hugh, king of Provence (d. 947), who wished to make himself king of Italy. Such an agreement was made in Mantua in 926. But Marozia was not to be outmaneuvered in this struggle for papal dominance. In 925 she married Guy, marchese of Tuscany, another influential Italian ruler who was the half brother of Hugh. Like his brother, Guy was a descendant of the royal house of Charlemange of the Carolingians, or Carlovingian, Dynasty. Guy loved his beautiful wife Marozia and also loved power. He had at his disposal a military force that could help execute Marozia's schemes. Together they moved on Rome, which at that time was governed by Roman consul, the Marchese Peter, brother of Pope John X. Peter had received the consular ppositionafter the death of Alberico I.
The pontificate of John X was now drawing to a close. guy's troops entered Rome. As the pope watched, Peter was "cut to pieces" by Guy; john was imprisoned in a dungeon in the Castle Sant' Angelo, and soon after (in 928) Guy suffocated him with a pillow. Marozia was now in full command of Rome. She was enobled with the titled "senatrix" and "patricia," and with her husband, she ruled Rome in effect, placing thrre popes on the papal throne - Leo VI (928), Stephen VII (929-31) and her own son John XI (931-35), who was only in his early twenties when elected. John XI became a tool to be used by his mother.
When Guy of Tuscany died in 929, Marozia did not wish to remain a widow for long. Needing a new power base, she quickly offered her hand in marriage to King Hugh of Provence. In 932 the marriage was performed in Castle Sant' Angelo, blessed by Pope John XI. After the marriage Hugh was to receive the imperial crown. It was the culmination of Marozia's aspiration of supreme power, She would become empress.
But during these festivities the unexpected was to happen. hugh became increasingly arrogant, treating the Roman nobility with comtempt. Further, this marriage between in-laws (Hugh and Guy were half brothers), prohibited by the church, had profoundly offended the moral sense of Rome. It had also infuriated Marozia's son Alberico II, who had been informed that his new stepfather intended to blind him so that he would not become a rival to the imperial throne. As the festivities progressed, Marozia asked her son to pour some water for Hugh to wash his hands. In the process some water may have spilled - Hugh, claiming that his stepson had shown disrespect, slapped Alberico's face. Alberico left the castle and called upon Romans to revolt against this alien who was married to his mother and was to become lord of Rome. The Romans responded, attacking and seizing the castle in December 932. hugh barely ascaped and fled the city.
Even though he was to threaten Rome from time to time, Hugh was thenceforth to play an inconsequential role in the history of Rome, dying in 947. The consequences for Marozia of the poplar revolt of the Roomans were even more devastating. She was handed over to Alberico II, her son, who imprisoned his mothr in the dungeons of Castle Sant' Angleo to disappear from history. Her domination of Rome had come to an abrupt end, Marozia died in obscurity before 937.
