* This investigation is supported by the National Science Foundation G. 9654. 1 Brauer, R., and M. Suzuki, "On Finite Groups of Even Order Whose 2-Sylow Group is a Quaternion Group," these PROCEEDINGS, 45, 1757-1759 (1959). 2 Feit, W., "On Groups Which Contain Frobenius Groups as Subgroups," Proc. Symp. Pure Math., 1, 22-28 (1959). 3 Feit, W., M. Hall, and J. Thompson, "Finite Groups in Which t...

We study δ-derivations – a construction simultaneously generalizing derivations and centroid. First, we compute δ-derivations of current Lie algebras and of modular Zassenhaus algebra. This enables us to provide examples of Lie algebras having 1 2 -derivations which are divisors of zero, thus answering negatively a question of Filippov. Second, we note that δ-derivations allow, in some circumst...

vasil'ev posed problem 16.26 in [the kourovka notebook: unsolved problems in group theory, 16th ed.,sobolev inst. math., novosibirsk (2006).] as follows:does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphicnonabelian finite simple groups with the same graphs of primes? conjecture: $k = 5$.in [zvezdina, on nonabelian simple groups having the same prime gr...

let $p$ be a complex polynomial of the form $p(z)=zdisplaystyleprod_{k=1}^{n-1}(z-z_{k})$,where $|z_k|ge 1,1le kle n-1$ then $ p^prime(z)ne 0$. if $|z|

Assuming that every proper minor closed class of graphs contains a maximum with respect to the homomorphism order, we prove that such a maximum must be homomorphically equivalent to a complete graph. This proves that Hadwiger’s conjecture is equivalent to saying that every minor closed class of graphs contains a maximum with respect to homomorphism order. Let F be a finite set of 2-connected gr...

Let Fq be the finite field with q elements, A := Fq[T ] and F := Fq(T ). Let φ be a Drinfeld A-module over F with trivial endomorphism ring. We prove analogues of the Erdös and Halberstam Theorems for φ. If φ has rank ≥ 3, we assume the validity of the Mumford-Tate Conjecture for φ. 1

Through an h̄-expansion of the confined Calogero model with spin exchange interactions, we extract a generating function for the involutive conserved charges of the FrahmPolychronakos spin chain. The resulting conservation laws possess the spin chain yangian symmetry, although they are not expressible in terms of these yangians. 08/00 (revised: 02/01) 1 Work supported by NSERC (Canada) and FCAR ...