Eg. Goodaire et Cp. Miles, FINITE SUBLOOPS OF UNITS IN AN ALTERNATIVE LOOP RING, Proceedings of the American Mathematical Society, 124(4), 1996, pp. 995-1002
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).