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Greece skipper Giorgos Karagounis, who played his 120th match for national team, scored the solitary goal of the game in the end of the first half.
This result helped Greece to collect four points and qualify to play-offs of the Euro-2012 from the second place.
In the second match of the Group A, the Czech Republic defeated co-host Poland and claimed the first place in the group. Petr Jiracek netted the goal on 72 minutes.