the probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. several authors have investigated this notion with methods of the representation theory and with combinatorial techniques. here we illustrate that a wider context may be considered and show some structural restrictions on the group.

BACKGROUND Active transportation has been associated with favorable health outcomes. Previous research highlighted the influence of neighborhood educational level on active transportation. However, little is known regarding the effect of commuting distance on social disparities in active commuting. In this regard, women have been poorly studied. The objective of this paper was to evaluate the r...

‎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...

Let $K$ be a subgroup of finite group $G$ . The probability that an element commutes with is denoted by $Pr(K,G)$ Assume $Pr(K,G)\geq \epsilon$ for some fixed $\epsilon >0$ We show there normal $T\leq G$ and $B\leq K$ such the indices $[G:T]$ $[K:B]$ order commutator $[T,B]$ are $\epsilon$ -bounded. This extends well-known theorem, due to P. M. Neumann, covers case where $K=G$ deduce number ...

This paper analyzes the relation between commuting time and specific health outcomes using the GSOEP and the BHPS. Both countries are in the top three of European countries in which commuting time is largest. First, we analyze whether commuting time affects specific health outcomes. We analyze both subjective health outcomes like health satisfaction and health status, and objective measures lik...

"This paper analyses whether the basic monocentric model of urban structure and commuting explains actual commuting in Europe, i.e. The Netherlands. As in the USA much wasteful commuting is established. The basic model has a low degree of explanatory power. In order to get more in line with actual commuting, the paper elaborates two alternatives to the basic model. Besides a deconcentrated mode...

Previous research has shown that households are sensitive to commuting distance. In particular, households beyond a threshold distance move closer to the job when they change residence. The questions which motivate this paper are-how does race affect the probability of moving closer to the job when households change residence, and is there a trade off between commuting distance and neighborhood...

Let $G$ be a finite group, let $p$ prime and ${\rm Pr}_p(G)$ the probability that two random $p$-elements of commute. In this paper we prove Pr}_p(G) > (p^2+p-1)/p^3$ if only has normal abelian Sylow $p$-subgroup, which generalizes previous results on widely studied commuting group. This bound is best possible in sense for each there are groups with = classify all such groups. Our proof based b...

We discuss the definition of quantum probability in the context of “timeless” general–relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multi-event probability. In conventional quantum mechanics this can be obtained by means of the “wave function collapse” algorithm. We first point out certain difficulties of some natural definitions of multi-eve...