* Rape victim's body cremated soon after arrival
* Protests in Delhi city centre
* Six suspects charged with murder
* New alleged gang rape outside Kolkata, police say
By Adnan Abidi and Devidutta Tripathy
NEW DELHI, Dec 30 (Reuters) - The body of a woman, whose gang rape provoked protests and rare national debate about violence against women in India, arrived back in New Delhi on Sunday and was cremated at a private ceremony.
Scuffles broke out in central Delhi between police and protesters who say the government is doing too little to protect women. But the 2,000-strong rally was confined to a single area, unlike last week when protests raged up throughout the capital.
Riot police manned barricades along streets leading to India Gate war memorial - a focal point for demonstrators - and, at another gathering point - the centuries-old Jantar Mantar - protesters held banners reading "We want justice!" and "Capital punishment".
Most sex crimes in India go unreported, many offenders go unpunished, and the wheels of justice turn slowly, according to social activists, who say that successive governments have done little to ensure the safety of women.
The unidentified 23-year-old victim of the Dec. 16 gang rape died of her injuries on Saturday, prompting promises of action from a government that has struggled to respond to public outrage.
The medical student had suffered brain injuries and massive internal injuries in the attack and died in hospital in Singapore where she had been taken for treatment.
She and a male friend had been returning home from the cinema, media reports say, when six men on a bus beat them with metal rods and repeatedly raped the woman. The friend survived.
New Delhi has the highest number of sex crimes among India's major cities, with a rape reported on average every 18 hours, police figures show. Reported rape cases rose by nearly 17 percent between 2007 and 2011, according to government data.
Six suspects were charged with murder after her death and face the death penalty if convicted.
In Kolkata, one of India's four biggest cities, police said a man reported that his mother had been gang-raped and killed by a group of six men in a small town near the city on Saturday.
She was killed on her way home with her husband, a senior official said, and the attackers had thrown acid at the husband, raped and killed her, and dumped her body in a roadside pond.
Police declined to give any further details. One officer told Reuters no criminal investigation had yet been launched.
The leader of India's ruling Congress party, Sonia Gandhi, was seen arriving at the airport when the plane carrying the woman's body from Singapore landed and Prime Minister Mannmohan Singh's convoy was also there.
A Reuters correspondent saw family members who had been with her in Singapore take her body from the airport to their Delhi home in an ambulance with a police escort.
Her body was then taken to a crematorium and cremated. Media were kept away but a Reuters witness saw the woman's family, New Delhi's chief minister, Sheila Dikshit, and the junior home minister, R P N Singh, coming out of the crematorium.
The outcry over the attack caught the government off guard. It took a week for the prime minister to make a statement, infuriating many protesters. Last weekend they fought pitched battles with police.
Issues such as rape, dowry-related deaths and female infanticide rarely enter mainstream political discourse.
Analysts say the death of the woman dubbed "Amanat", an Urdu word meaning "treasure", by some Indian media could change that, though it is too early to say whether the protesters can sustain their momentum through to national elections due in 2014.
U.N. Secretary General Ban Ki-Moon added his voice to those demanding change, calling for "further steps and reforms to deter such crimes and bring perpetrators to justice".
Commentators and sociologists say the incident earlier this month has tapped into a deep well of frustration many Indians feel over what they see as weak governance and poor leadership on social issues.
Newspapers raised doubts about the commitment of both male politicians and the police to protecting women.
"Would the Indian political system and class have been so indifferent to the problem of sexual violence if half or even one-third of all legislators were women?" the Hindu newspaper asked.
The Indian Express said it was more complicated than realising that the police force was understaffed and underpaid.
"It is geared towards dominating citizens rather than working for them, not to mention being open to influential interests," the newspaper said. "It reflects the misogyny around us, rather than actively fighting for the rights of citizens who happen to be female."