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Let Cl(O K [G]) denote the locally free class group, that is the group of stable isomorphism classes of locally free O K [G]-modules, where O K is the ring of algebraic integers in the number field K and G is a finite group. We show how to compute the Swan subgroup, , ζp a primitive p-th root of unity, G = C 2 , where p is an odd (rational) prime so that h + p = 1 and 2 is inert in K/Q. We show that, under these hypotheses, this calculation reduces to computing a quotient ring of a polynomialdoi:10.1090/s0025-5718-00-01302-8 fatcat:ufpumyj7yvdytn5s2ebvex7ywe