This preview shows page 1. Sign up to view the full content.
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 a-1 -s, and there are exactly as many b -s as b-1 -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 )[ aa-1 = a-1 a = e ] ( b G )[ bb-1 = b-1 b = e ]...
View Full Document
- Spring '08