The effect of an involution inwidetilde{K}^0 (ZG)

The involution in the Grothendieck group of the group ring of a finite cyclic group of prime order p, induced by the transition to the contragredient module is identical to complex conjugation followed by the automorphism x x^–1 in the ideal class group of the cyclotomic field of order p.Russian article translated from the English by V. L. Golo.Translated from Matematicheskie Zametki, Vol. 3, No. 5, pp. 523–528, May, 1968.