Other SP candidates who filed nomination are former Legislative Council Chairman Sukhram Singh Yadav, Reoti Raman Singh and Vishwambhar Prasad Nishad.
Among those who filed their nomination papers for SP, Seth is a 'controversial' builder from Lucknow. His name was earlier sent by the party to Raj Bhawan for nomination as an MLC, but it was not approved by Governor Ram Naik.
While Amar Singh was in political wilderness for six years following his expulsion from SP, Beni recently returned to the party fold after quitting Congress.
Amar Singh was accompanied by his wife and two daughters while filing his nomination. Senior party leaders Shivpal Yadav and Ram Gopal Yadav were also present.
Chief Minister Akhilesh Yadav, who was in Bhadohi on an official visit, and SP supremo Mulayam Singh Yadav were conspicuous by their absence.
The support of 37 MLAs is needed for a candidate's entry into Rajya Sabha.
As per the existing strength of different parties in the 403-member state Assembly, SP with 229 MLAs would be able to get six nominees elected to Rajya Sabha, BSP two and BJP one. Currently, BSP has six of these seats and SP three.
Eight SP candidates for the UP Legislative Council -- Balram Yadav, Shatrudra Prakash, Yashwant Singh, Bukkal Nawab, Ram Sundar Das, Jagjivan Ram, Kamlesh Pathak and Rajvijay Singh -- also filed their nominations.
The biennial elections are slated to be held next month.
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Later, talking to mediapersons, Amar Singh said, he would "utilise the opportunity to strengthen the Samajwadi Party" while thanking SP supremo Mulayam Singh Yadav.
Party general secretary Ramgopal Yadav said, "The party will be strengthened after the RS and MLC polls."
On being asked about two years of the Narendra Modi government at the Centre, Yadav called it an "utter failure".