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Slot, who also faced a hefty fine after an independent commission found him accountable for the fracas at the end of the contentious 2-2 draw with Everton on February 12, saw red after squaring up to Oliver.
His assistant Sipke Hulshoff didn't escape punishment either and he was hit with a matching two-game suspension.
The official FA statement read: "An independent Regulatory Commission has sanctioned Everton, Liverpool, Arne Slot and Sipke Hulshoff in relation to the Premier League fixture between the clubs on Wednesday 12 February.
"It was alleged that both clubs failed to ensure their players and/or technical area occupants did not behave in an improper and/or provocative way following the final whistle
Everton and Liverpool admitted the charges, and the Regulatory Commission imposed £65,000 ($82,000) and £50,000 fines ($63,000) on them respectively following a hearing.
"It was alleged that the Liverpool head coach acted in an improper manner and/or used insulting and/or abusive words and/or behaviour towards both the match referee and an assistant referee after the match had finished
Arne Slot admitted the charge, and the Regulatory Commission imposed a two-match touchline suspension and £70,000 ($89,000) fine.
"It was alleged that the Liverpool assistant head coach acted in an improper manner and/or used insulting and/or abusive words and/or behaviour towards a match official, which led to his dismissal
It was further alleged that he acted in an improper manner and/or used insulting and/or abusive words and/or behaviour towards a match official after being sent off
Sipke Hulshoff admitted the charge, and the Regulatory Commission imposed a two-match touchline suspension and £7,000 ($9,000) fine.
"The Regulatory Commission's written reasons for these sanctions will be published in due course."
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