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Saturday, November 7, 2009

Watched lecture 7 of Abstract Algebra E-222

Gross formulated the following question: Can we put a group structure on the set of cosets {aH} for a subgroup H in G? He subsequently based the entire lecture on answering this ( simple ) question. The answer is ( of course ) yes if H is normal in G.

At the end, briefly for students with an interest in Algebraic Topology, Gross mentioned sequences like 1 -> H -> G -> G' -> 1.  With examples 1 -> Z3 -> Z6 -> Z2 -> 1 and 1 -> A3 -> S3 -> {1,-1} -> 1 which show that by knowing  Z3 ~ A3 and Z2 ~ {1,-1} does not say anything about the resultgroup.

Basicly a long abstract theoretical discussion about factorgroups, with basicly zero examples. How will group theory develop in people exposed to such lectures? I am not sure if I want to think about that.

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