We study the commuting graph on elements of odd prime order in finite simple groups. The results are used in a forthcoming paper describing the structure of Bruck loops and Bol loops of exponent 2.

Let X and Y be commuting nilpotent K-endomorphisms of a vector space V , where K is a field of characteristic p ≥ 0. If F = K(t) is the field of rational functions on the projective line P1/K , consider the K(t)-endomorphism A = X+ tY of V . If p = 0, or if A = 0, we show here that X and Y are tangent to the unipotent radical of the centralizer of A in GL(V ). For all geometric points (a : b) o...

OBJECTIVE Automobile dependency and longer commuting are associated with current obesity epidemic. We aimed to examine the urban-rural differential effects of neighborhood commuting environment on obesity in the US METHODS: The 1997-2005 National Health Interview Survey (NHIS) were linked to 2000 US Census data to assess the effects of neighborhood commuting environment: census tract-level auto...

The quantity g (k) (v) was introduced in [6] as the minimum number of blocks necessary in a pairwise balanced design on v elements, subject to the condition that the longest block has length k. Recently, we have needed to use all possibilities for such minimal covering designs, and we record all non-isomorphic solutions to the problem for v ≤ 13.

Time shifts beyond the correlation time of the logic and reference signals create new elements that are orthogonal to the original components. This fact can be utilized to increase the number of dimensions of the logic space while keeping the number of reference noises fixed. Using just a single noise and time shifts can realize exponentially large hyperspaces with large numbers of dimensions. ...

In this paper the space of commuting elements in the central product Gm,p of m copies of the special unitary group SU(p) is studied, where p is a prime number. In particular, a computation for the number of path connected components of these spaces is given and the geometry of the moduli space Rep(Z, Gm,p) of flat principal Gm,p–bundles over the n–torus is completely described for all values of...