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.

Author Bio

I am a senior mathematics major at Siena College and junior mechanical engineering majorat Rensselaer Polytechnic Institute. This work was a summer research project carried out under the supervision of Dr. JonBannon at Siena College.