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Mahak Sharma

Publications and source records attributed to Mahak Sharma.

6 recordsLinked to original sources
arXiv2025

On the conjecture of non-inner automorphisms of finite $p$-groups with a non-trivial abelian direct factor

Let $p$ be a prime number. A longstanding conjecture asserts that every finite non-abelian $p$-group has a non-inner automorphism of order $p$. In this paper, we prove that the conjecture is true when a finite non-abelian $p$-group $G$ has a non-trivial abelian direct factor. Moreover, we prove that the non-inner automorphism is central and fixes $\Phi(G)$ elementwise. As a consequence, we prove that every group which is not purely non-abelian has a non-inner central automorphism of order $p$ which fixes $\Phi(G)$ elementwise.

math.GR↗
arXiv2024

On the conjecture of non-inner automorphisms of finite $p$-groups

Let $p$ be a prime number. A longstanding conjecture asserts that every finite non-abelian $p$-group has a non-inner automorphism of order $p$. In this paper, we prove that if $G$ is an odd order finite non-abelian monolithic $p$-group such that every maximal subgroup of $G$ is non-abelian and $[Z(M), g] \leq Z(G)$ for every maximal subgroup $M$ of $G$ and $g \in G \setminus M$. Then $G$ has a non-inner automorphism of order $p$ leaving the Frattini subgroup $\Phi(G)$ elementwise fixed.

math.GR↗
arXiv2021

Communication is the universal solvent: atreya bot -- an interactive bot for chemical scientists

Conversational agents are a recent trend in human-computer interaction, deployed in multidisciplinary applications to assist the users. In this paper, we introduce "Atreya", an interactive bot for chemistry enthusiasts, researchers, and students to study the ChEMBL database. Atreya is hosted by Telegram, a popular cloud-based instant messaging application. This user-friendly bot queries the ChEMBL database, retrieves the drug details for a particular disease, targets associated with that drug, etc. This paper explores the potential of using a conversational agent to assist chemistry students and chemical scientist in complex information seeking process.

cs.HC↗
arXiv2014

Class-preserving automorphisms of some finite $p$-groups

Let $G$ be a finite $p$-group of order $p^5$, where $p$ is a prime. We give necessary and sufficient conditions on $G$ such that $G$ has a non-inner class-preserving automorphism. As a consequence, we give short and alternate proofs of results of section 5 of Yadav [Proc. Indian Acad. Sci. (Math. Sci.) 118 (2008), 1-11] and Theorem 4.2 of Kalra and Gumber [Indian J. Pure Appl. Math. 44 (2013), 711-725].

math.GR↗
arXiv2011

On central automorphisms of finite p-groups

We characterize all finite p-groups G of order p^n(n\leq 6), where p is a prime for n\leq 5 and an odd prime for n = 6, such that the center of the inner automorphism group of G is equal to the group of central automorphisms of G.

math.GR↗