Unformatted text preview: H , namely a n H . (So we can modify set arithmetic on cosets using containment. This wrinkle comes up again in 150b when defining quotient rings.) GK2. As I will have said in class, if G is a group and H is a subgroup, then G and H are equiconjugate if they have this property: If a , b ∈ H are conjugate in G , then they are also conjugate in H . (Actually I made up this word; I do not know the official terminology.) Is the tetrahedral group T equiconjugate with the rotation group SO ( 3 ) ? Is the octahedral group O equiconjugate with SO ( 3 ) ? (The groups T and O are defined in section 5.9.) *GK3. How many isometries does an ndimensional cube possess? (As a subgroup of O ( n ) , say.)...
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 Spring '03
 Kuperberg
 Algebra, Group Theory, Normal subgroup, Coset, Modern Algebra Homework

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