Pradeep Kumar Rai Assistant Professor Department of Mathematics

Dr. Pradeep Kumar Rai is an Assistant professor of Mathematics at Mahindra University. Previously he was an INSPIRE Faculty at Harish-Chandra Research Institute Prayagraj. Before this, he was an INSPIRE Faculty at IIT Patna and spent a couple of years as a PBC Post-Doctoral Fellow at Bar-Ilan University Israel. He has received a Ph.D. degree from Harish-Chandra Research Institute Allahabad. His area of research is finite group theory. His PhD thesis is about the automorphisms of groups. It studies class-preserving automorphisms of groups and prime power groups with abelian automorphism groups. His post-doctoral work derives bounds on the order of the Schur multiplier of prime power groups improving earlier bounds and classifies groups having Schur multipliers of maximum order. 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.
His publications include Pradeep K. Rai, On Bogomolov multiplier and X-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, Arch. Math. (Basel), Vol 111 (2018), 129- 133. Pradeep K. Rai, On Schur multiplier of special p-groups, J. Pure Appl. Algebra., 222 (2018), 316-322.

  • Education
    • Ph.D., Mathematics - Harish-Chandra Research Institute, Allahabad, India, December 2014 (Submission), August 2015 (Defense)
      Thesis: Automorphisms of groups.
    • M.Sc., Mathematics - Indian Institute of Technology Bombay, June 2008
    • B.Sc., - Ewing Christian College, University of Allahabad, June 2006.
  • Research
    • Partial Differential Equations (PDE) based Image Processing
    • Finite Difference Method for Differential Equations
  • Publications
    • Pradeep K. Rai, On Bogomolov multiplier and X-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, Arch. Math. (Basel), Vol 111 (2018), 129- 133. 
    • Pradeep K. Rai, On Schur multiplier of special p-groups, J. Pure Appl. Algebra., 222 (2018), 316-322.
    • Pradeep K. Rai, A Note on the order of the Schur multiplier of p-groups, Int. J. Algebra Comput., Vol 27 (2017), 495-500.
    • Pradeep K. Rai, On the classification of groups having Schur multiplier of maximum order, Arch. Math. (Basel), Vol 107 (2016), 455-460. 
    • Pradeep K. Rai, On nilpotency of a group of outer class-preserving automorphisms of groups, J. Algebra Appl., 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 X-rigidity of groups of order p 6, J. Algebra, Vol 428 (2015), 26-42. 
    • Pradeep K. Rai, On IA-automorphisms that fix the centre 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, Internat. J. of Algebra Comput., Vol 23, No.35 (2013), 1063-1077. Preprints 1. Pradeep K. Rai, On the order of the Schur multiplier of finite p-groups. 
  • Experience

    Teaching Experience

    • Taught Algebraic Topology to M.Sc. and Ph.D. Students at IIT Patna
    • Taught General Topology to M.Sc. Students at IIT Patna

    Research Experience

    • DST-INSPIRE Faculty, Sept 2019 to 2021
      Harish-Chandra Research Institute, Allahabad, India.
    • DST-INSPIRE Faculty, July 2017 to August 2019.
      Department of Mathematics, IIT Patna, Bihar, India.
    • PBC Post-Doctoral Fellow, October 2015 to June 2017.
      Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel.