FINITE SUBLOOPS OF UNITS IN AN ALTERNATIVE LOOP RING

An RA loop is a loop whose loop rings, in characteristic different fro m 2, are alternative but not associative. In this paper, we show that every finite subloop H of normalized units in the integral loop ring o f an RA loop L is isomorphic to a subloop of L. Moreover, we show that there exist units gamma(i) in the rational loop algebra QL such that gamma(k)(-1)(...(gamma(2)(-1)(gamma(1)(-1)H(gamma 1))(gamma 2)...))(ga mma k) subset of or equal to L. Thus, a conjecture of Zassenhaus which is open for group rings holds for alternative loop rings (which are n ot associative).