A 35-year-old guitarist has been released on police bail after questioning over the murder of schoolteacher Jane Longhurst.
The man, who lives with a female friend of Jane's in Hove, was arrested on Thursday evening. He is said to deny any involvement in the murder.
The man has played guitar with a number of tribute bands.
His entry on the Friends Reunited web site reads: "Living in Brighton and making a rather enjoyable and interesting living from being a musician."
Neighbours saw police officers arrive in the street on Thursday night. One said: "You see police down here from time to time anyway so I didn't take much notice."
A barman at a local pub said: "Police came in asking questions about a man. I know of the couple but that's about all."
A mechanic who runs a workshop nearby said he regularly serviced the man's girlfriend's car.
He said: "She is a very pleasant woman but I have never spoken to him. I was totally amazed when I heard."
Officers spent all of Friday examining the couple's flat and officers remained on guard outside on Saturday.
Jane, 31, who taught at Uplands School for children with learning difficulties in Hollingdean, disappeared from her home in Shaftesbury Road, Brighton, on March 14.
Her body was discovered on fire at Wiggonholt Common, near Pulborough, on Easter Saturday. She had been strangled.
Police this weekend continued searching for Jane's Nokia mobile phone, her Next purse, keys, denim jacket and red suede shoes.
They are also trying to trace a brown or green Ford Focus seen at Wiggonholt Common when Jane's body was found.
A week on, officers were stopping motorists near the site on Saturday. A police spokesman said: "Officers will be stopping vehicles as part of the operation to trace potential witnesses.
"Detectives are emphasising that they still want to hear from people who were at or near the beauty spot on Easter Saturday."
The Argus is offering a £5,000 reward for information leading to the arrest and conviction of the killer.
Anyone with information should contact Operation Keen on 0845 6070999.
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