Defence Secretary Philip Hammond has named the pilot killed in Tuesday's Tornado crash as Flight Lieutenant Hywel Poole.
Squadron Leader Samuel Bailey and Flight Lieutenant Adam Sanders are still missing presumed dead.
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Political parties across the country suspended their General Election campaigns following the Manchester Arena terror attack on Monday.
Investigators believe Mr Kushner has significant information relevant to their inquiry, officials told NBC News.
The men were detained as part of an investigation by MI5 and the Metropolitan Police's Counter Terrorism Command.