‎we consider two commutativity ratios $pr(g)$ and $f(g)$ in a finite group $g$‎ ‎and examine the properties of $g$ when these ratios are `large'‎. ‎we show that‎ ‎if $pr(g) > frac{7}{24}$‎, ‎then $g$ is metabelian and we give threshold‎ ‎results in the cases where $g$ is insoluble and $g'$ is nilpotent‎. ‎we also‎ ‎show that if $f(g) > frac{1}{2}$‎, ‎then $f(g) = frac{n+1}{2n}$‎, ‎for some‎ ‎na...

This paper, deals with some equivalence relations in fuzzy subgroups. Further the probability of commuting two fuzzy subgroups of some finite abelian groups is defined.

Abstract For any (Hausdorff) compact group G , denote by $\mathrm{cp}(G)$ the probability that a randomly chosen pair of elements commute. We prove there exists finite H such $\mathrm{cp}(G)= {\mathrm{cp}(H)}/{|G:F|^2}$ where F is FC-centre and isoclinic to with $\mathrm{cp}(F)=\mathrm{cp}(H)$ whenever $\mathrm{cp}(G)>0$ . In addition, we $\mathrm{cp}(G)>\tfrac {3}{40}$ either solvable or...

The article aims to discuss the concept of commuting probability for finite groups, which in short, is a measure how abelian our group is. We shall compute value many special classes groups and also establish some local global bounds. will conclude with few topics further reading.

this paper, deals with some equivalence relations in fuzzy subgroups. further the probability of commuting two fuzzy subgroups of some finite abelian groups is defined.

The author studies trends in commuting to the city of Zagreb in Croatia, Yugoslavia. Commuter surveys and bivariate analysis are used to describe the socioeconomic level, occupational status, transportation method, and place of residence of rural and urban residents who commute to the city. (SUMMARY IN ENG AND RUS)

This paper focuses on the effects of commuting time on sickness insurance utilization by applying a generalized propensity score estimator to a large sample of Swedish employees. We analyse the effect of commuting time both on the probability of using sickness insurance at all and on the probability that an individual on sick leave is on so-called partial sick leave rather than being completely...

‎Suppose $n$ is a fixed positive integer‎. ‎We introduce the relative n-th non-commuting graph $Gamma^{n} _{H,G}$‎, ‎associated to the non-abelian subgroup $H$ of group $G$‎. ‎The vertex set is $Gsetminus C^n_{H,G}$ in which $C^n_{H,G} = {xin G‎ : ‎[x,y^{n}]=1 mbox{~and~} [x^{n},y]=1mbox{~for~all~} yin H}$‎. ‎Moreover‎, ‎${x,y}$ is an edge if $x$ or $y$ belong to $H$ and $xy^{n}eq y^{n}x$ or $x...