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math.GR2026
On Conjugacy Classes of Derangements in Symmetric and Alternating Groups
Harish Kishnani, Rijubrata Kundu
In this article, we prove two conjectures of Burness and Fusari [Timothy Burness and Marco Fusari, On derangements in simple permutation groups, Forum Math. Sigma 13 (2025)] concer…
math.RA2026
Waring Problem for matrices over finite local rings
Ram Karan Choudhary, Harish Kishnani, Anupam Singh
This paper addresses the matrix Waring problem for matrices over finite principal local rings. Let be a finite principal local ring of length with the m…
math.RA2026
Images of Lie Polynomials on simple Lie algebras
Harish Kishnani, Anupam Singh
A Lie polynomial is an element of a free Lie algebra on -generators, which defines a Lie map on a given Lie algebra , by substituting -elements of . Simi…