Rejecting reports the bomber had recently returned to Britain from Libya, Mr Abedi said his son Salman had visited Libya more than a month ago. Speaking from Tripoli, Mr Abedi told the Associated Press: "We don't believe in killing innocents. This is not us." Mr Abedi confirmed his son Ismail, who was born in Westminster in 1993, was arrested on Tuesday.

The Special Deterrence Force in Libya is under the Department of Interior. Here is their Facebook page and the announcement of Hassam Abedi's arrest (there's a translate feature.) It says he confessed. Who wouldn't after being arrested by them? Text of their statement (translated by Facebook) below:

The Special Deterrent Force has been able to arrest one of the suspects with the authority of the state of ISIS, which lasted for almost a month and a half until the information received from the investigation teams was up to act as a terrorist act in the capital city of Tripoli.

The Information was presented to Mr. Head of the investigations section of the attorney general's office, which ordered the suspect to be arrested as soon as possible, and on 23-5-2017, he was arrested approximately 23-5-2017 p.m.
The arrest was promptly received during the receipt of an estimated $ 4500 million. To be funded by guy,.

After the initial interrogation, he said:

Hashim Ramadan Abu Al-Qasim Al-denominator

Born in 8.4.1997 in Manchester English.
University student in Manchester UK
He also reported that he was a member of the state of ISIS with his brother / Salman Al-Labidi and admitted to his presence in Britain during the preparation period and found out he was fully aware of the details of this terrorist operation
It's worth mentioning that he came out of Britain on 16.4.2017th and admitted that he was on constant contact with his sister.

(my emphasis - translation error?)

These Libyan security forces are pretty confusing and I know nothing about Libya. Abedi's father is reportedly the administrative manager for one of them, the Central Security force in Tripoli, which is loyal to Haithem Tajouri, while the one that arrested him and his son is called the Special Deterrence Force which is based at the airport in Tripoli. Since Libya is a mess of competing factions, I have no idea whether one is considered more legitimate than the other. I did find this description, but have no idea as to the reliability of the source:

Rada forces (special deterrence forces – قوة الردع الخاصة) are the main security force in Tripoli in the sense they are not perceived as a political militia subverting the state but the opposite, despite the salafist denomination of it’s leadership Abdurraouf Kara. They operate as an independent department under the MOI minister directly, and implement a focused anti-narcotics & OC mandate, do actual police work; patrols, investigations and arrests and are relatively well disciplined. They are probably the 3rd largest force in the city in terms of arms 4th in terms of size, after Haithem Tajouri’s forces (1st Company – MOI Central Security Department), Nawasi, (Rada) and Ghniwa’s Abu Saleem Military Council (now integrated into the local security directorate of the municipality.

These are the main militias structured as ‘security’ forces inside the city. The reason Rada are smaller is 90% actual police officers (Lieutenant and above) 10% civilians, and around 70% of them pre-2011. Their jurisdiction is mainly limited to the east-southeast part of Tripoli where they have their branches and most of their forces; Tripoli centre, Soug Al Jouma, Ain Zara etc.

The New York Times reports:

The militia is affiliated with the United Nations-backed Government of National Accord, one of three administrations vying for control of Libya, but it has been accused by human rights groups of abusing prisoners under its control.

The British knew about Hassem Abedi because an article yesterday said he was suspected of writing supportive messages on a pro-IS website about now deceased ISIS fighter Ryeed Khan. Khan was killed in a UK drone strike in Syria.

According to the press release from the security forces, Hassem entered Libya on 4/16/17. Their father said Salman left a few weeks ago, to go to Saudi Arabia, and was then planning on returning to Libya for Ramadan. The French think he went to Syria at some point.

All of the Amedi children were born and raised in Great Britain. They are British citizens.

British police are now trying to trace Salman's steps. Since it was reported he arrived at the Manchester train station from London, it shouldn't be too hard. Unless it's not true. A pub owner today say police asked for his CCTV footage.

They also arrested a female on the 12th floor of a building in a block of flats in Blackley in Manchester. I wonder if that's his sister Jomana, or if she's in Libya. (Her FB page that many are quoting has not been updated since 2014.)

Lastly for now, media is speculating over a 50 year old al-Qaeda bombmaker, Abd al-Baset Azzouz, who left the UK in 2009 and was arrested in Turkey in 2014 and extradited to Jordan as being tied to Salman Abedi because he emigrated from Libya to the UK around 1993 and in 2000, lived on the same block as the Abedi family and after that, the families lived within a mile of each other (and most other Libyans in Manchester who had fled Ghadaffi.) From Jordan, he was reportedly transferred to the Libyan National Army a few weeks ago. I find that so unbelievably far-fetched I won't even link to the article.

What happened to the reports he traveled from London to Manchester by train just before entering the Arena? That came from U.S. officials according to Reuters. Some are now saying he left London a few days before the attack. And there is footage of him shopping on Friday at a Manchester mall carrying the blue blackpack with the price tag still on it. More here.

Did he even go to London at all? Stay tuned.