Tim Hsu
We obtain the following results on Moufang loops L of class 2:
A. The nuclearly-derived subloop of L has exponent dividing 6. In particular, when L is finite, the p-part of L is associative for p>3.
B. L is said to be small Frattini (an "SFML") if L has a central subgroup of order p such that L/Z is an elementary abelian p-group. We show that SFML's are classified by "coded vector spaces".
C. We show that every SFM 2-loop is a code loop.
D. We obtain a characterization of isotopy in SFM 3-loops which is easily extended to Moufang loops of class 2 and exponent 3.
E. We sketch a construction for any finite Moufang loop of class 2.