Note 4 — Chapter I · THE VIKINGS IN IRELAND (795-1014).
Reading edition
Some writers would identify Turgeis with Thorgils, son of Harold Fairhair, who with his brother Frothi went on a viking expedition to Ireland. They captured Dublin, and Thorgils reigned there for a long time as king. In the end, however, he was betrayed by the Irish and was killed. (Heimskringla: Haralds saga hins hárfagra, ch. 35.)
This account of Thorgils certainly bears a resemblance to that of Turgeis contained in the Irish chronicles and Giraldus Cambrensis (cf. Todd: Introduction to War of the Gaedhil with the Gaill, I., ii.), but it is of course incorrect to say that Turgeis was a son of Harold Fairhair.