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Parama Dutta

Publications and source records attributed to Parama Dutta.

11 recordsLinked to original sources
arXiv2021

On r-noncommuting graph of finite rings

Let $R$ be a finite ring and $r\in R$. The $r$-noncommuting graph of $R$, denoted by $Γ_R^r$, is a simple undirected graph whose vertex set is $R$ and two vertices $x$ and $y$ are adjacent if and only if $[x,y] \neq r$ and $-r$. In this paper, we study several properties of $Γ_R^r$. We show that $Γ_R^r$ is not a regular graph, a lollipop graph and complete bipartite graph. Further, we consider an induced subgraph of $Γ_R^r$ (induced by the non-central elements of $R$) and obtained some characterizations of $R$.

math.RA↗
arXiv2019

On Deficient Perfect Numbers with Four Distinct Prime Factors

For a positive integer $n$, if $σ(n)$ denotes the sum of the positive divisors of $n$, then $n$ is called a deficient perfect number if $σ(n)=2n-d$ for some positive divisor $d$ of $n$. In this paper, we prove some results about odd deficient perfect numbers with four distinct prime factors.

math.NT↗
arXiv2017

On relative commuting probability of finite rings

In this paper we study the probability that the commutator of a randomly chosen pair of elements, one from a subring of a finite ring and other from the ring itself equals to a given element of the ring.

math.RA↗
arXiv2017

On relative autocommutativity degree of a subgroup of a finite group

In this paper, we consider the probability that a randomly chosen automorphism of a finite group fixes a randomly chosen element of a subgroup of that group. We obtain several new results as well as generalizations and improvements of some existing results on this probability.

math.GR↗
arXiv2017

Laplacian Spectrum of non-commuting graphs of finite groups

In this paper, we compute the Laplacian spectrum of non-commuting graphs of some classes of finite non-abelian groups. Our computations reveal that the non-commuting graphs of all the groups considered in this paper are L-integral. We also obtain some conditions on a group $G$ so that its non-commuting graph is L-integral.

math.GR↗
arXiv2017

Autocommuting probability of a finite group relative to its subgroups

Let $H \subseteq K$ be two subgroups of a finite group $G$ and Aut$(K)$ the automorphism group of $K$. The autocommuting probability of $G$ relative to its subgroups $H$ and $K$, denoted by ${\rm Pr}(H, {\rm Aut}(K))$, is the probability that the autocommutator of a randomly chosen pair of elements, one from $H$ and the other from Aut$(K)$, is equal to the identity element of $G$. In this paper, we study ${\rm Pr}(H, {\rm Aut}(K))$ through a generalization.

math.GR↗
arXiv2017

Autocommuting probability of a finite group

Let $G$ be a finite group and $\Aut(G)$ the automorphism group of $G$. The autocommuting probability of $G$, denoted by $\Pr(G, \Aut(G))$, is the probability that a randomly chosen automorphism of $G$ fixes a randomly chosen element of $G$. In this paper, we study $\Pr(G, \Aut(G))$ through a generalization. We obtain a computing formula, several bounds and characterizations of $G$ through $\Pr(G, \Aut(G))$. We conclude the paper by showing that the generalized autocommuting probability of $G$ remains unchanged under autoisoclinism.

math.GR↗
arXiv2016

On commuting probability of finite rings II

The aim of this paper is to study the probability that the commutator of an arbitrarily chosen pair of elements, each from two different subrings of a finite non-commutative ring equals a given element of that ring. We obtain several results on this probability including a computing formula, some bounds and characterizations.

math.RA↗