Geodesic
The Schur Subgroup of a p-Adic Field
Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 300-303

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Let K be a field. The Schur subgroup, S(K), of the Brauer group, B(K), consists of all classes [△] in B(K) some representative of which is a simple component of one of the semi-simple group algebras, KG, where G is a finite group such that char K ∤ G. Yamada ([11], p. 46) has characterized S(K) for all finite extensions of the p-adic number field, Qp . If p is odd, [△] ∈ S(K) if and only if where c is the tame ramification index of k/Qp , k the maximal cyclotomic subfield of K, and s = ((p – 1)/c, [K : k]). invp △ is the Hasse invariant. Yamada showed this by proving first that S(K) is the group of classes containing cyclotomic algebras and then determining the invariants of such algebras. 
Spiegel, Eugene; Trojan, Allan. The Schur Subgroup of a p-Adic Field. Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 300-303. doi: 10.4153/CJM-1979-031-5
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