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In the other Group E tie, Bulgarian side CSKA Sofia were held 1-1 at home by England's Fulham.
CNN: Hamburg humbled in Europa League by Rapid
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The result sees Fulham progress from Group E alongside Roma, who won 3-0 at CSKA Sofia to finish top of the pool.
BBC: FC Basle 2-3 Fulham
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Paris-born Kamara has started just five league games for Fulham this season, scoring once, and struck against CSKA Sofia in the Europa League.
BBC: Celtic sign Fulham's Kamara, Braafheid and Well's Slane
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The result left Roma in third place on four points, while Swiss side Basel went top on six following a 2-0 victory away to CSKA Sofia.
CNN: Ranieri's Roma snatch draw at 10-man Fulham
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The result saw Fulham relinquish their place at the top of Group E to Basle, who beat CSKA Sofia 2-0, although Roy Hodgson's side remain unbeaten in the competition.
BBC: Fulham 1-1 Roma
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Roma coach Claudio Ranieri got the result he was after from his players after they ended a run of disappointing results with a 2-0 victory over CSKA Sofia to register their first points in Group E .
CNN: Werder Bremen go clear in Europa Cup group
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But the newly promoted Tangerines, who make their Premier League bow at Wigan on Saturday, announced on Wednesday the capture of Manchester United's Craig Cathcart, Elliot Grandin from CSKA Sofia, Monaco's Malaury Martin and and Ludovic Sylvestre from Czech side Mlada Boleslav.
BBC: Blackpool boss Ian Holloway dismisses quit rumours