Unformatted text preview: theory (basically, that a symbol and its inverse next to each other cancel out). For a precise list of relations, see below. Prove that the commutator subgroup of G is the set of strings in which there are exactly as many ‘ a ’s as ‘ a1 ’s, and there are exactly as many ‘ b ’s as ‘ b1 ’s (including among them the identity itself). List of relations in F ( a, b ) (writing e for the identity) ( ∀ a ∈ G )[ ea = ae = a ] ( ∀ a ∈ G )[ aa1 = a1 a = e ] ( ∀ b ∈ G )[ bb1 = b1 b = e ]...
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 Spring '08
 ctw
 Math, Group Theory, commutator subgroup, usual multiplicative notation

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