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Four members of the same family have been arrested after a nine-year-old boy was beaten to death at his home in the eastern French city of Mulhouse.

Police sources told local media that the boy had refused to do his homework and was hit with a broom handle.

The boy's elder brother, sister and stepsister were all present at the time of the incident.

Although his mother was not there, she too has been arrested and was aware of what was going on, reports say.

The boy's death in September prompted a vigil in the centre of Mulhouse among residents who rallied round his parents.

But the family's initial accounts of what had happened and the ensuing post-mortem examination prompted police to continue their investigation. Bruises were discovered on the boy's body, particularly on his feet, according to Alsace website DNA.

Although he had suffered a cardiac arrest, pathologists said the cause of death had been the blows he had suffered, DNA reported.

A police source was quoted as saying he had been struck by blunt objects.

The boy's mother had been away from home on a business trip but had actively encouraged his punishment because he did not want to do his homework, French media said.

The four members of the family were being held in custody in Mulhouse on Thursday and were due to appear before the local prosecutor ahead of a judicial investigation.

Although the 19-year-old elder brother is suspected of carrying out the killing, an investigating judge will try to shed further light on the tragedy.

The boy's death comes at a time when France's National Assembly is about to consider a ban on smacking.

The two proposals are for children to be entitled to an education free of violence, and for those in parental authority to be banned from using "means of humiliation such as physical or verbal violence, corporal punishment and moral abuse".