Class 2 Moufang loops, small Frattini Moufang loops, and code loops
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 $p\gt3$.
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.