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Homework due March 19.
Do the following problems in Greenberg and Harper: 5.9, 5.11, 5.12, 6.13, and 6.14.
For 5.9 you need the definition of the normalizer of a subgroup H of a group G.
6.13 relies on the description of the special orthogonal group SO(3) given in 6.12, which is interesting in its own right. Here is an extra credit problem, also due on March 19:
Prove that SO(4) (the group of 4x4 orthogonal matrices with determinant 1) is homeomorphic to S^3 x RP^3, the product of the 3-sphere with projective 3-space.Unfortunately there are no similar descriptions of the higher orthogonal groups in terms of more familiar spaces.