Claims have included suggestions of incidents in the Ruffs Drive and George Street areas of Hucknall and Bestwood Park.
Several of the posts suggested that the police had been informed and some even go on to say people have been detained or arrested.
But Nottinghamshire Police say they have received no reports of any incidents and have moved to reassure people that they should not panic.
The reports and rumours even prompted Edgewood Primary School in Hucknall to put out a blanket text to parents, warning them to be on their guard.
However, after speaking with the police, the school said they were happy there had been nothing reported.
Ed Seeley, headteacher at the school, said they were acting solely with the safety of their pupils in mind and he was glad it turned out there was no need for concern.
He explained: “We got the report from a parent who had reported it to the school. We’ve since spoken to the police who say there are no records of any crimes related to this.
“We wanted to act quickly to safeguard our children and ensure that, if this had happened, then nothing could happen to anybody else.
“But we have since followed up with the police and they have no record of any such crime.
“We were given information that was very detailed and seemed very plausible and we were just acting to safeguard children and make sure that if this was happening, parents were aware and could keep them safe.
“We’d far rather it was a false alarm and nothing was happening and our children were safe.”
And the increasing alarm being caused on social media has led to police appealing for calm.
A Nottinghamshire Police spokesperson said: “When things are reported on social media it doesn’t necessarily mean they are true.
“If anyone has any concerns, they should contact the police directly on 101.”
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