Dr. Pradeep Kumar Rai is an Associate Professor of Mathematics at Ecole Centrale School of Engineering, Mahindra University. He received his Ph.D. in Mathematics from Harish-Chandra Research Institute, Allahabad in 2015. Later he worked as a PBC Post-Doctoral Fellow in Bar-Ilan University, Israel (2015-2017). Prior to joining Mahindra University he held the position of INSPIRE Faculty at Harish-Chandra Research Institute, Prayagraj (2019-2021) and Indian Institute of Technology Patna (2017-2019). His area of research is Group Theory. His Ph.D. thesis is about the automorphisms of groups. It studies class-preserving automorphisms, and prime power groups having abelian automorphism group. His more recent work is about second cohomology group of prime power groups. These works have been published in journals such as Journal of Algebra, Journal of Pure and Applied Algebra, International Journal of Algebra and Computation and others.

• Ph.D. in Mathematics: Harish-Chandra Research Institute, Allahabad
  December 2014 (Submission), August 2015 (Defense).
• M.Sc. in Mathematics: Indian Institute of Technology Bombay, June 2008.
• B.Sc. in Mathematics & Computer Applications: Ewing Christian College, University of Allahabad, June 2006.

• Pradeep K. Rai, Bounds on the order of the Schur multiplier of finite p-groups, Journal of Pure and Applied Algebra, Volume 228, Issue 1, January 2024, 107463.
• Pradeep K. Rai, Bogomolov multiplier of Lie algebras, Linear Algebra and its Applications, Volume 672, (2023), 122-133.
• Pradeep K. Rai, On the occurrence of elementary abelian p-groups as the Schur multiplier of non-abelian p-groups, Comptes Rendus Mathematique, Volume 361 (2023), 803-806.
• Pradeep K. Rai, On Bogomolov multiplier and $\Sha$-rigidity of groups, Journal of Algebra, Vol. 534 (2019), 384-391.
• Pradeep K. Rai, On the dimension of the Schur multiplier of nilpotent Lie algebras, Communications in Algebra, Vol. 47 (2019), 3982-3986.
• Pradeep K. Rai, On the classification of groups having Schur multiplier of maximum order II, Archive der Mathematik (Basel), Vol 111 (2018), 129- 133.
• Pradeep K. Rai, On Schur multiplier of special p-groups, Journal of pure and applied algebra, 222 (2018), 316-322.
• Pradeep K. Rai, A Note on the order of the Schur multiplier of p-groups, International Journal of Algebra and Computation, Vol 27 (2017), 495-500.
• Pradeep K. Rai, On the classification of groups having Schur multiplier of maximum order, Archive der Mathematik (Basel), Vol 107 (2016), 455-460.
• Pradeep K. Rai, On nilpotency of a group of outer class-preserving automorphisms of groups, Journal of Algebra and its Application, Vol 15 (2016).
• Pradeep K. Rai, On commuting automorphisms of finite p-groups, Proc. Japan Acad. Ser. A Math. Sci, Vol 91 (2015), 57-60.
• Pradeep K. Rai and Manoj K. Yadav, On $\Sha$-rigidity of groups of order p 6, Journal of Algebra, Vol 428 (2015), 26-42.
• Pradeep K. Rai, On IA-automorphisms that fix the center elementwise, Proc. Indian acad. Sci. (Math. Sci.), Vol 124, No.2 (2014), 169-173.
• Pradeep K. Rai, On class-preserving automorphisms of groups, Ricerche Mat., Vol 63 (2014), 189-194.
• Vivek K. Jain, Pradeep K. Rai and Manoj K. Yadav, On finite p-groups with abelian automorphism group, International Journal of Algebra and Computation, Vol 23, No.35 (2013), 1063-1077.

• DST-INSPIRE Faculty, Sept 2019 to July 2021,
  Harish-Chandra Research Institute, Allahabad, India.
• Visiting Position, October 2018 to July 2019,
  Indian Institute of Science Education and Research Mohali, Punjab, India.

• DST-INSPIRE Faculty, July 2017 to August 2019,
  Department of Mathematics, Indian Institute of Technology Patna, Bihar, India.

• PBC Post-Doctoral Fellow, October 2015 to June 2017,
  Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel.

• Group Theory: Cohomology Groups of prime power groups and automorphisms of groups.