A remark concerning a theorem of B. Friedman

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

A remark concerning graphical sequences

In “A note on a theorem of Erdös & Gallai” ([6]) one identifies the nonredundant inequalities in a characterization of graphical sequences. We explain how this result may be obtained directly from a simple geometrical observation involving weak majorization. A sequence of positive integers d1, d2, . . . , dp is called graphical if it is the degree sequence of a graph, i.e., there is a graph who...

The Friedman Embedding Theorem

In this paper, we will present an explicit construction of Harvey Friedman which to every finitely generated group G associates a 2-generator subgroup KG 6 Sym(N) such that G embeds into KG and such that if G ∼= H, then KG = KH .

a remark on a remark by macaulay or enhancing lazard structural theorem

A Remark on Zoloterav’s Theorem

Let n ≥ 3 be an odd integer. For any integer a prime to n, define the permutation γ a,n of {1,. .. , (n − 1)/2} by γ a,n (x) = n − {ax} n if {ax} n ≥ (n + 1)/2, {ax} n if {ax} n ≤ (n − 1)/2, where {x} n denotes the least nonnegative residue of x modulo n. In this note, we show that the sign of γ a,n coincides with the Jacobi symbol a n if n ≡ 1 (mod 4), and 1 if n ≡ 3 (mod 4).