THE AUTOMORPHISMS OF NON-DEFECTIVE ORTHOGONAL GROUPS IN CHARACTERISTIC 2

Let V be a non-defective n-dimensional quadratic space over a field F of characteristic2.In this paper we prove that,when n≥6 with n≠8 and F≠F_2,any automorphism ofΩ(V)orO'(V)has the standard type Φ_g,sending σ to gσg~(-1),where g is a semilinearautomorphism of V which preserves the quadratic structure.Therefore the automorphismgroups Aut Ω(V) and Aut O'(V)are isomorphic to PΓO(V).As a corollary,Aut O(V)and Aut O~+(V) are isomorphic to PΓO(V)as well.     

THE AUTOMORPHISMS OF NON-DEFECTIVE ORTHOGONAL GROUPS Ω_8(V)AND O'_8(V)IN CHARACTERISTIC 2

Let V be a non-defective 8-dimensional quadratic space over a field F of characteristic2,F≠F_2.We prove that if there is an exceptional automorphism of either Ω_8(V)orO'_8(V),then V~a has a Cayley algebra structure for some a in .Moreover,everyexceptional automorphism of O'_8(V)as exactly one of the following forms:_1°Φ_g or 2°Φ_g,where Φ_g is an automorphism of O'_8(V)given by conjugation by a semilinear automorphismof V which preserves the quadratic structure,and _1 and _2 are the automorphismsinduced by triality principle.Every exceptional automorphism of Ω_8(V)is the restrictionof a unique exceptional automorphism of O'_8(V).     

ON IDEAL CLASS GROUPS AND UNITS IN TERMS OF THE QUADRATIC FORM x^2＋32y^2

§1. IntroductionIt is a classical topic to study, for quadratic number ?elds F = Q(√2p) with a prime p,the exact 2-power dividing the narrow class number h (F) and the norm of the fundamentalunit ε of F.The 2-primary subgroup of the narrow class group …     

EXISTENCE AND UNIQUENESS OF STRONG PERIODIC SOLUTION OF THE EVOLUTION SYSTEM DESCRIBING GEOPHYSICAL FLOW—PART I： IN BOUNDED DOMAINS

61. IntroductionDiscovered by R. HideI3], the following evolution system has been used to describe thegeophysical flow:where u = u(xl,',XN,t) = (ul,',UN) and B = B(xl,',XN,t) = (BI,',BN) arethe velocity vectors Of Eulerian flow and magnetic fields respectively. p(x, t) and q(x, t) arepressures. j(x, t) and g(x,t) are volUme forces. p and u are the constants of density andviscosity of the flow respeCtively, p is the constant of magnetic permeability and A = f withelectrical resis…