**Dr. Deepak Gumber**

Finite Groups, Automorphisms of Finite Groups

Sr.No. | Sponsor | Title of Project | Duration | Grant Amount |
---|---|---|---|---|

1. | UGC | Automorphisms of Finite p-Groups | 2014-17 | 60 Lakhs |

2. | NBHM | Non-Inner and Class-Preserving Automorphisms of Finite p-Groups | 2014-17 | 10.11 Lakhs |

3. | SERB, DST | Divisibility Conjecture and Existence of Non-Inner Automorphisms of Order p for Non-Abelian Finite p-Groups | 2016-19 | 20.56 Lakhs |

Sr.No. | Name of Student | Title of Thesis | Year |
---|---|---|---|

1. | Hemant Kalra | Automorphisms of Finite p-Groups | 2013 |

2. | Mahak Sharma | Central and Class-Preserving Automorphisms of Finite p-Groups | 2015 |

3. | Sandeep Singh | Automorphisms of Finitely Generated Groups | 2016 |

- Sandeep Singh and Deepak Gumber, Automorphism groups of finitely generated groups that are isomorphic to the group of inner automorphisms, Quaestiones Mathematicae (to appear).
- Mahak Sharma, Hemant Kalra and Deepak Gumber, Some finite p-groups with central automorphism group of non-minimal order, J. Algebra Appl. 17(2) (2018) 1850026 (5 pages).
- Sandeep Singh and Deepak Gumber, A note on commuting automorphisms of finite p-groups, Math. Notes 100(5) (2016), 755- 757.
- Sandeep Singh, Deepak Gumber and Hemant Kalra, Erratum: IA-automorphisms of finitely generated nilpotent groups, J. Algebra Appl. 15(7) (2016), 1692002 (2 pages).
- Deepak Gumber and Hemant Kalra, Equality of certain automorphism groups of finite p-groups, J. Algebra Appl. 15(3) (2016), 1650056 (7 pages).
- Sandeep Singh and Deepak Gumber, Finite p-groups whose absolute central automorphisms are inner, Math. Commun. 15 (2015), 1-6.
- Deepak Gumber and Hemant Kalra, The conjugacy class number k(G): a different perspective, Comm. Algebra, 43(11) (2015), 4836-4838.
- Mahak Sharma and Deepak Gumber, Class-preserving automorphisms of some finite p-groups, Proc. Indian Acad. Sci. (Math. Sci.), 125(2) (2015), 181-186.
- Deepak Gumber and Hemant Kalra, Finite p-groups with central automorphism group of minimal order, Comm. Algebra, 43(5) (2015), 1802-1806.
- Sandeep Singh, Deepak Gumber and Hemant Kalra, IA-automorphisms of finitely generated nilpotent groups, to appear in J. Algebra Appl.
- Hemant Kalra and Deepak Gumber, A note on conjugacy classes of finite groups, to appear in Proc. Indian Acad. Sci. (Math. Sci.).
- Deepak Gumber and Hemant Kalra, On the converse of a theorem of Schur, Arch. Math., 101 (2013) 17-20.
- Mahak Sharma and Deepak Gumber, On central automorphisms of finite p-groups, Comm. Algebra, 41 (2013) 1117-1122.
- Hemant Kalra and Deepak Gumber, On equality of central and class preserving automorphisms of finite p-groups, Indian J. Pure Appl. Math., 44(5) (2013) 711-725.
- Deepak Gumber, Some applications of augmentation quotients, Hacet. J. Math. Stat., 42 (6) (2013) 627-631.
- Deepak Gumber, An intersection theorem in free group rings, Int. J. Algebra, 4 (2010) 769-775.
- Deepak Gumber, Ram Karan and Indu Pal, Some augmentation quotients of integral group rings, Proc. Indian Acad. Sci. (Math. Sci.) 118 (2008) 537-546.
- Ram Karan and Deepak Kumar, Augmentation quotients of free group rings, Algebra Colloq., 12 (2005) 597-606.
- Ram Karan, Deepak Kumar and L. R. Vermani, Some intersection theorems and subgroups determined by certain ideals in integral group rings, II, Algebra Colloq., 9 (2002) 135-142.
- Ram Karan and Deepak Kumar, Some intersections and identifications in integral group rings, Proc. Indian Acad. Sci. (Math. Sci.), 112 (2002) 289-297.

- UGC Research Award in 2013
- CSIR Junior and Senior Research Fellowship during PhD
- University Research Fellowship during PhD
- Haryana State Merit Scholarship during MA

- Finite p-groups with central automorphism group of minimal order, Discussion Meeting on Group Theory, May 8-11, 2014, IISER, Mohali.
- A Note on Conjugacy Classes of Finite Groups, International Conference on Group Theory and Lie Theory (GT & LT-2012), March 19-21, 2012, Harish-Chandra Research Institute, Jhunsi, Allahabad.
- Augmentation Quotients of Integral Group Rings, Colloquium on Recent Trends in Algebra and Algebraic Number Theory, November 25-27, 2009, Center for Advanced Studies in Mathematics, Panjab University, Chandigarh.

- Attended and presented a paper entitled “On Class Preserving Automorphisms of Groups of Order 32” in “International Workshop cum Conference on Groups, Actions, Computations-2010” held from Sep. 10-12, 2010 in Harish Chandra Research Institute, Allahabad.
- Presented a paper entitled “An Intersection Theorem in Free Group Rings” in “International Conference on Algebra and its Applications” held from Nov. 13-16, 1997 in Dept. of Mathematics, Aligarh Muslim University, Aligarh.
- Presented a paper entitled “Some Intersection Theorems and Subgroups Determined by Certain Ideals in Integral Group Rings” in “Sixth Ramanujan Symposium on Algebra and its Applications” held from Feb. 24-26, 1999 in Ramanujan Institute for Advanced Study in Mathematics, University of Madras.
- Attended “International Conference on Algebra and its Applications” held from Nov. 13-16, 1997 in Dept. of Mathematics, Aligarh Muslim University, Aligarh.