Fréttatíminn, Iceland (CNN) Birna Brjánsdóttir, the Reykjavik native whose murder has shocked Iceland, should have been safe walking alone after a night out with friends, but she wasn't.

Described as a kind, fun-loving redhead with a great sense of humor, the 20-year-old sales assistant, whose funeral takes place on Friday, was last seen alive early on the morning of January 14.

The final trace of her was caught on surveillance video as she stumbled along the city's main street. She passed several CCTV cameras before stepping out of the last frame and disappearing into the night. A week later, her body washed up on a desolate beach outside of the Icelandic capital.

Home to only 300,000 people, Brjánsdóttir's murder has gripped Iceland -- a country with one of the lowest murder rates in the world. Iceland has gone entire years -- 2003, 2006, and 2008 -- without any murders at all, according to local reports

Thousands of mourners gathered in the capital last weekend, re-tracing Brjánsdóttir's steps. Her route crossed the same street that plays host each summer to Iceland's annual SlutWalk protest, a march for women's rights.

The disappearance of the young woman who wore Doc Martens and dark lipstick defied Iceland's ongoing fight for women's rights, rattling the island nation where women generally feel safe walking home alone at night.

A mother's grief

It was her mother Sigurlaug Hreinsdottir's outcry that convinced the police something unusual had happened.

When Brjánsdóttir didn't show up at work on Saturday, her phone switched off, Hreinsdottir knew something was wrong. Her daughter was usually never out of touch.

Her family immediately reported her missing.

The news swiftly began to spread and a photograph of the young woman circulated on social media.

Brjánsdóttir's mother speaks with the press.

The search for Brjánsdóttir became unusually public after a news conference at the Metropolitan Police headquarters in which her mother appealed to the public for answers. In every shop, on every bus and in every workplace across the country people began speculating, trying to figure out what had happened to Brjánsdóttir.

The police had traced her phone to Hafnarfjordur, a port town on the outskirts of Reykjavik, half an hour after she vanished.

They released footage from security cameras showing an unidentified red Kia Rio sedan driving by the spot where Brjánsdóttir was last seen alive. The police asked the driver, who they believed might be a key witness, to come forward.

A policeman hugs Brjánsdóttir's mother.

"I think she might have gone into a car with someone she didn't know," Brjánsdóttir's mother said, emphasizing that her daughter had not run away.

"Someone knows where she is and I think someone is keeping her. It's very unlike her to go into hiding. She isn't depressed and she isn't involved with drugs."

A breakthrough

The first breakthrough came when Brjánsdóttir's black Doc Martens were found on a dock at the harbor of Hafnarfjordur.

Soon the red rental car was traced to two sailors from the Greenlandic trawler Polar Nanoq. The ship had been docked in the Hafnarfjordur port, a few hundred meters from where Brjánsdóttir's shoes were discovered. Video surveillance also showed the same car parked near the vessel at 6am, on the morning of her disappearance.

Hundreds of volunteers participated in a huge search and rescue effort to find Brjánsdóttir.

Over 700 people from across the country volunteered to help with a complex search and rescue operation -- the largest ever in Icelandic history, according to Landsbjörg, the Icelandic Association for Search and Rescue.

They covered over 7000 km in cold and stormy weather before the operation was suddenly stopped on Sunday, January 22. Another news conference was set.

Search and rescue workers looking for traces of Brjánsdóttir.

Police revealed that Brjánsdóttir's body had been spotted from a helicopter on a rocky black beach in the Reykjanes peninsula, about an hour drive from the capital.

Reykjavik police arrested two Greenlandic sailors after traces of Brjánsdóttir's blood were found splattered in their rental car -- the red Kia Rio sedan. The men are the prime suspects in Brjánsdóttir's death, believed by police to have brutally murdered her and dumped her remains into the ocean. One of the men was released on Thursday, but is still suspected of involvement in the murder. The other remains in custody.

Confronting prejudices

When it became clear that the suspects in the case were from Greenland, Icelanders were forced to confront their deeply rooted prejudices against the indigenous people in the neighboring country.

Police arrest two Greenlandic sailors suspected of involvement in Brjánsdóttir's murder.

"There was a tendency amongst Icelanders to look down on Greenlanders," Icelander Embla Kristjánsdóttir, head of department at The Ministry of Municipalities in Greenland, said in an interview.

"People in Nuuk express to me how deeply saddened they are by the tragic events. It's moving to witness how strongly connected they are to Icelanders. Their pain is no less than ours."

In response to the murder, a few hundred Greenlanders gathered at the Icelandic consulate in Nuuk, braving -17°C (1.4°F) temperatures to light candles in a memorial to Brjánsdóttir.

A few hundred people gathered in a vigil for Brjánsdóttir outside the Icelandic consulate in Nuuk, Greenland.

Jørgen Fossheim, fleet manager at the fishery that operates the vessel Polar Nanoq, offered his condolences to Brjánsdóttir's family and friends. Polar Nanoq donated 1,6 million ISK (about $14,000) to the staff and volunteers who worked "tirelessly" to find Brjánsdóttir, according to Landsbjörg, which shared Fossheim's letter on their Facebook page.

The strong response from Greenlanders after Brjánsdóttir's disappearance has forced Icelanders to look inwards and reflect.

Thousands of mourners gathered in Reykjavik.

Among the thousands who marched in Reykjavik last weekend to honor Brjánsdóttir's life was Iceland resident Sigrídur Hrund Gudmundsdóttir.

"My children are the same age as her," Gudmundsdóttir told the Icelandic Broadcasting Service, RÚV. "So much has been taken away from us and we feel less safe after this."

'Remembering Birna

Funeral services for Brjánsdóttir will be held in Reykjavik on Friday afternoon. After intense media scrutiny, her family has asked for privacy at the memorial, so that they can honor Brjánsdóttir in peace.

Friends, family members, and others touched by Brjánsdóttir's case have already begun memorializing her with posts on social media, with many sharing the words: "Ég er Birna" (I am Birna). The refrain is a sign of how deeply Brjánsdóttir's loss is felt by Icelanders.

Matthildur Soffía Jónsdóttir shared a series of photos and videos of her friend, Brjánsdóttir, on Facebook after learning of her death.

"I would never have thought that I would lose my best friend, especially not this way," Jónsdóttir wrote. "I'm angry, sad and angry. She wasn't supposed to go like this, nobody deserves to go like this."