Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1994. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 22)

KIRÁLY, B., On the powers of the augmentation ideal of a group ring

Ori the powers of the augmentation ideal of a group ring 83 Theorem 3.4. Let R be a commutative ring of non-zero characteristic n and let the augmentation terminal of G with respect to R be finite. Then T

r(G)= max {

r (<?)}= maX {T°(A(R

P

IG/G

P

I))} > p,en(n) p;6ll(n) > max {T

P

i (G)} . Pi en (n) PROOF. By Theorem 3.2 we have that max {r

R (G)) = p.Gn(n)

1 max {T°(A(R

P

IG/G

P

I))}> max {R

P

I(G)}. From (6) and (9) we have Pi Gll(n) ' ' pi 6ll(n) that T

R(G)= max {R

R (G)} which was to be proved. PiGlIfn) P

l References [1] BOVDI, A. A., Group rings, UMK VO, KIEV

, 1988. [2] GRUENBERG, K. W., ROSEBLADE, J. E., The augmentation terminais of certain locally finite groups, Can. J. Math., XXIV, 2., (1972), 221238. [3] HARTLEY, B., The residual nilpotence of wreath products, Proc. London Math. Soc., (3) 20, (1970), 365-392. [4] PASSI, I. B., Group ring and their augmentation ideals, Lecture notes in Math., 715, Springer-Verlag, BerlinHeidelberg-New York, 1979. [5] SEHGAL, S. K., Topics in group rings, Marcel Dekker, Inc., New York and Basel, 1978.