A bench headed by Chief Justice Dipak Misra said these convicts - Mukesh (31), Pawan Gupta (24) and Vinay Sharma (25) - have failed to point out any "error apparent on the face of record" in the judgement and they were given elaborate hearing during their appeal against the Delhi High Court judgement.
The fourth man convicted in the case, Akshay Thakur, did not file an appeal but his lawyer says he plans to do so.
Explaining that review jurisdiction is exercised by the court in case of "glaring omission or injustice", justice Ashok Bhushan decreed that the present case did not disclose any ground for interfere.
"If, notwithstanding the view of the abolitionists to the contrary, a very large segment of people, the world over, including sociologists, legislators, jurists, judges and administrators still firmly believe in the worth and necessity of capital punishment for the protection of society", the apex court said.
On 16 December 2012, the six convicts raped and brutalised the student in a moving bus she had boarded in South Delhi with a male friend. She died two weeks later of injuries in a hospital in Singapore, where she had been taken for treatment.
The sixth defendant, a minor accused of pulling out part of the woman's intestines with his own hand, was sent to a reform home for three years and has since been released.More news: Gareth Southgate says England can become immortal like 1966 heroes
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The victim's father said, "All women in the country have received justice today".
SC dismisses review of death sentences of three of the four men convicted of killing 23-year-old.
"There is no evidence to show that the death penalty acts as a deterrent for sexual violence or any other crime", said Asmita Basu, a top official of the global rights organisation in India. If this petition is also rejected, a mercy plea would be their last option. Their sentence was upheld by the Delhi high court in 2014.
In its previous judgement, the SC had said that "the brutal, barbaric and diabolic nature" of the crime was capable of creating "a tsunami of shock" that could destroy a civilised society.
The girl from the northern Jammu region died after being kidnapped, drugged and gang raped by several men for days at a Hindu temple.
In April 2018, the Centre had approved an ordinance introducing death penalty for those convicted of raping girls aged 12 years or younger, it said.
Out of the 371 death row convicts in 2017, 43 were awarded the punishment for crimes involving fatal sexual assaults.