According to the complainant, a 56-year-old Andheri resident, the Facebook account on which the obscene comment was posted is in the name of a Shiv Sena (UBT) activist.
According to the police, the complainant is the coordinator of the CM Eknath Shinde-led Shiv Sena for the Andheri assembly constituency.
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"She came across the obscene comment while reading a news report online. The post was intended to insult the modesty of a woman," the official said.
Based on the complaint lodged by the Andheri-based woman, the Mumbai Police registered a case under sections 509 (word, gesture or act intended to insult the modesty of a woman ), 153- A (1) (Promoting enmity between two groups) of the IPC and the Information Technology Act.
This is the second offence registered against Shiv Sena (UBT) activists in the three days.
Meanhwile, in another incident between the two Sena faction, Aaditya thackeray lashed out at Maharashtra CM Eknath Shinde after an FIR was registered against him for illegally inaugurating the Delisle Road Bridge in Lower Parel.
On Saturday, the Shiv Sena (UBT) leader Aaditya Thackeray stated that the government and the Chief Minister himself are "illegal and immoral."
"I think what is laughable is that this government itself is illegal. So who are they declaring illegal? As a result of my tweet, they opened the metro to the public...It is my constituency but I didn't say that we did this or they did this. I just said that the CM who is illegal, and immoral has no time for the public, for such projects. So, we should open this for the public," Aaditya Thackeray said.
(with inputs from agencies)