Rajat Kanti Nath

A NEW CLASS OF ALMOST MEASURE PRESERVING MAPS ON FINITE SIMPLE GROUPS

In this paper, we give a new class of almost equidistributed and almost measure preserving maps on finite simple groups as the order of the group tends to infinity. This answers an open problem posed by Shalev.

A generalization of commutativity degree of finite groups

The commutativity degree of a finite group is the probability that two arbitrarily chosen group elements commute. This notion has been generalized in a number of ways. The object of this article is to study yet another generalization of the same notion, which further extends some of the existing generalizations.

On the probability distribution associated to commutator word map in finite groups

In this paper, we study the probability distribution associated to the commutator word map. In other words, we study the probability of a given element of a group to be equal to a commutator of two randomly chosen group elements. We compute explicit formulas for calculating this probability for some interesting classes of groups having only two different conjugacy class sizes.

COMMUTATIVITY DEGREE OF A CLASS OF FINITE GROUPS AND CONSEQUENCES

The commutativity degree of a finite group is the probability that two randomly chosen group elements commute. The object of this paper is to compute the commutativity degree of a class of finite groups obtained by semidirect product of two finite cyclic groups. As a by-product of our result, we provide affirmative answer to an open question posed by P. Lescot. 10.1017/S0004972712001086

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 so that its non-commuting graph is L-integral.

Autocommuting probability of a finite group

ABSTRACT 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.

A generalization of commuting probability of finite rings

The aim of this paper is to study the probability that the commutator of an arbitrarily chosen pair of elements, each from two different additive subgroups 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.