Dr. Sugandha Maheshwary
Inspire Faculty, Mathematical Sciences

Email sugandha(AT)iisermohali.ac.in  
Fax +91 172 2240266
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Research Area:  Group rings and their structure

Research Focus:

 

Given a group G and a field K, it is a fundamental problem to determine the structure of group algebra KG. The focus of my research has been on determining the structure of KG, in case it is semisimple and to study the related applications which include determining the automorphism group of finite group algebra F G and better understanding of the unit group of inte- gral group ring ZG. The study of units and central units of ZG came into light in 1940 with work of G.Higman and is still topic of intensive research. We have obtained some interesting results in the same and look forward to contributing further. In particular, we studied cut-groups, i.e., the groups G which have all central units of ZG trivial. We aim at exploring more about upper and lower central series of the unit group of an integral group ring. It also interests me to write computational algorithms based the above mentioned work for GAP, which is a System software for Computational Discrete Algebra. Based on the work done during doctoral thesis, we contributed some functions to a GAP package Wedderga, which stands for Wedderburn decomposition of group algebras. I would like to continue the process of programs implementation further as well.
Selected Publications
  • S. Maheshwary, Integral group rings with all central units trivial: solvable groups, Indian J. Pure Appl. Math. 49(1) (2018), 169-175.
  • G. K. Bakshi, S. Maheshwary and I. B. S. Passi, Integral group rings with all central units trivial, J. Pure Appl. Algebra 221 (2017), 1955-1965.
  • G. K. Bakshi and S. Maheshwary, On the index of a free abelian sub- group in the group of central units of an integral group ring, J. Algebra 434(2015), 72-89.
  • G. K. Bakshi and S. Maheshwary, The rational group algebra of a normally monomial group, J. Pure Appl. Algebra 218 (2014), no. 9, 1583-1593.