We prove that the free Burnside Group B(3,2) has order 27 and is isomorphic to < a,b | a3, b3 (ab)3, (b-1a)3 > . The technique of our proof is also used to show that < a,b | a3, b3, a2 (ba)nb2 > is a semidirect product Cn2+n+1 x C3.
"The Burnside Group B(3,2) as a Two-Relator Quotient of C3*C3,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 8:
2, Article 6.
Available at: https://scholar.rose-hulman.edu/rhumj/vol8/iss2/6