Abramenko competed at the 2005 World Championships in Ruka, Finland, where he was 25th. Abramenko made his World Cup debut on 8 January 2006, in Mont Gabriel, Canada. He placed eighteenth. Even though he was quite young and inexperienced, he competed at the 2006 Winter Olympics in Turin, Italy. In aerials, he did not advance, placing 27th in the qualifying round. On 6 March 2006, he won a silver medal at the 2006 World Junior Championships in Krasnoe Ozero, Russia. On 19 January 2008, Abramenko finished tenth at the World Cup event in Lake Placid, United States. He was among the best in four of seven competitions that season.