About: Cartan–Brauer–Hua theorem

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In abstract algebra, the Cartan–Brauer–Hua theorem (named after Richard Brauer, Élie Cartan, and Hua Luogeng) is a theorem pertaining to division rings. It says that given two division rings K ⊆ D such that xKx−1 is contained in K for every x not equal to 0 in D, either K is contained in the center of D, or K = D. In other words, if the unit group of K is a normal subgroup of the unit group of D, then either K = D or K is central .

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  • In abstract algebra, the Cartan–Brauer–Hua theorem (named after Richard Brauer, Élie Cartan, and Hua Luogeng) is a theorem pertaining to division rings. It says that given two division rings K ⊆ D such that xKx−1 is contained in K for every x not equal to 0 in D, either K is contained in the center of D, or K = D. In other words, if the unit group of K is a normal subgroup of the unit group of D, then either K = D or K is central . (en)
  • 抽象代數中，布勞威耳-加當-華定理是個有關除環的定理，以德國數學家理查德·布饒爾、法國數學家埃利·嘉當、以及中國數學家華羅庚命名。 給定兩個除環使得對於所有中非零的都有（亦即，的单位群是的单位群的正规子群），則要么被包含在的中心，要么。 (zh)
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  • In abstract algebra, the Cartan–Brauer–Hua theorem (named after Richard Brauer, Élie Cartan, and Hua Luogeng) is a theorem pertaining to division rings. It says that given two division rings K ⊆ D such that xKx−1 is contained in K for every x not equal to 0 in D, either K is contained in the center of D, or K = D. In other words, if the unit group of K is a normal subgroup of the unit group of D, then either K = D or K is central . (en)
  • 抽象代數中，布勞威耳-加當-華定理是個有關除環的定理，以德國數學家理查德·布饒爾、法國數學家埃利·嘉當、以及中國數學家華羅庚命名。 給定兩個除環使得對於所有中非零的都有（亦即，的单位群是的单位群的正规子群），則要么被包含在的中心，要么。 (zh)
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  • Cartan–Brauer–Hua theorem (en)
  • 布劳威尔-加当-华定理 (zh)
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