Sonlu cisimler üzerindeki vektör değişmezlerinin derecelerinin alt sınırları üzerine

ABSTRACT ON LOWER DEGREE BOUNDS FOR VECTOR INVARIANTS OVER FINITE FIELDS Uğur Madran M. S. in Mathematics Advisor: Prof. Dr. S.A. Stepanov September, 2000 The purpose of this thesis is to obtain a lower degree bound in modular invariant theory for a special case. More precisely, let G be any group and k be a finite field of positive characteristic p such that p divides |G|. We prove that if an invariant which has degree at most p- 1 with respect to each variable can be written as a polynomial in orbit sums of monomials, then the invariant ring A;[Vrm]G of m copies of the vector space V over k with dimV = n requires a generator of degree ^s=|. ^y > ^ provided that m > n where t and nx depends on the representation of G such that f^] < t < n+ 1 and 2 < ni < p. Keywords and Phrases: Modular invariant theory, finite field, finite group. m