Abstract
Let k be a totally real subfield of a cyclotomic extension of the rational field Q. Denote by S,(k) the subset of the Brauer group Br(k) of h consisting of those algebra classes which contain a simple component of the group algebraQ[G] of some finite group G. According to the Brauer-Speiser theorem, every element of SQ(k) has order at most two in Br(k). When h is the rational field Q, the structure of S,(k) h as been determined by Benard [l] and Fields [5]. That is, they have shown that every quaternion division algebra central over Q appears in some Q[G]. Let I be an arbitrary prime number, c a positive integer and & a primitive P-th root of unity. In this paper, we completely determine S,(R) when k is the maximal totally real subfield k,,, = Q(clC + 4;‘) of the cyclotomic field Q(&). Eamely, we shall prove the following:
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