On the Torsion Units of Some Integral Group Rings∗
نویسندگان
چکیده
It is shown that any torsion unit of the integral group ring ZG of a finite group G is rationally conjugate to a trivial unit if G = P o A with P a normal Sylow p-subgroup of G and A an abelian p′-group (thus confirming a conjecture of Zassenhaus for this particular class of groups). The proof is an application of a fundamental result of Weiss. It is also shown that the Zassenhaus conjecture holds for PSL(2, 7), the finite simple group of order 168. 2000 Mathematics Subject Classification: primary 16S34, 16U60; secondary 20D15
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