Let G be the symmetric group of degree n. ω(G) maximal size a subset S such that 〈x,y〉=G whenever x,y∈S and x≠y let σ(G) minimal family proper subgroups whose union is G. We prove both functions are asymptotically equal to 12(nn/2) when n even. This, together with result S. Blackburn, implies σ(G)/ω(G) tends 1 as n→∞. Moreover, we give lower bound n/5 on which independent classification finite ...

We give a simple condition for a linear recurrence (mod 2w) of degree r to have themaximal possible period 2w 1(2r 1). It follows that the period is maximal in the casesof interest for pseudo-random number generation, i.e. for 3-term linear recurrences de nedby trinomials which are primitive (mod 2) and of degree r > 2. We consider the enumera-tion of certain exceptional pol...

From CON(ZFC) we obtain: 1. CON(ZFC + 2" is arbitrarily large + there is a locally finite upper semilattice of size W2 which cannot be embedded into the Turing degrees as an upper semilattice). 2. CON(ZFC + 2" is arbitrarily large + there is a maximal independent set of Turing degrees of size Xl). Introduction. Let 6D denote the set of Turing degrees ordered under the usual Turing reducibility,...

We offer a new perspective on the splitting principle. We give an easy proof that applies to all classical types of vector bundles and in fact to G-bundles for any compact connected Lie group G. The perspective gives precise calculational information and directly ties the splitting principle to the specification of characteristic classes in terms of classifying spaces. In the algebraic topology...

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

In a recent paper [M], Mathon gives a new construction of maximal arcs which generalizes the construction of Denniston. In relation to this construction, Mathon asks the question of determining the largest degree of a non-Denniston maximal arc arising from his new construction. In this paper, we give a nearly complete answer to this problem. Specifically, we prove that when m ≥ 5 and m 6= 9, th...

In a recent paper [M], Mathon gives a new construction of maximal arcs which generalizes the construction of Denniston. In relation to this construction, Mathon asks the question of determining the largest degree of a non-Denniston maximal arc arising from his new construction. In this paper, we give a nearly complete answer to this problem. Specifically, we prove that when m ≥ 5 and m 6= 9, th...