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Laleh Shahravesh faces a £50,000 fine and has been separated from her daughter.
Tech firms will have responsibilities outlined in a mandatory 'duty of care'.
The legislation was rushed thorough weeks after the Christchurch mosque attacks.
The e-petition started by Margaret Georgiadou is the biggest ever on the Parliament website.
They had been told it was the "safest country in the world".
The group sang 'justice for the three and “shame on you' as officers surrounded them.
No one reported the video while it was being streamed live.
Peterborough MP will stand as an independent after she was expelled from Labour over speeding offence.
"There should be no safe spaces for terrorists to share and promote their extreme views.”
One man has been charged for murder and three other people have been detained in Christchurch after 49 people were killed in two mosque attacks. The attacks started during Friday prayers, with eyewitnesses reporting that the perpetrator entered and started shooting at random. The attack was streamed on Facebook. Prime Minister Jacinda Ardern has called it a terrorist attack.