We study the simple Moufang loop GLL(F(2)) and give a complete description of its lattice of subloops. (C) 2008 Elsevier Inc. All rights reserved.

For finite Moufang loops, we prove an analog of the first Sylow theorem giving a criterion for the existence of a p-Sylow subloop. We also find the maximal order of p-subloops in the Moufang loops that do not possess p-Sylow ...

We describe bases of free commutative Moufang loop with seven generators and calculate the order of this loop. (c) 2011 Published by Elsevier Inc.

We investigate polynomial identities on an alternative loop algebra and group identities on its (Moufang) unit loop. An alternative loop ring always satisfies a polynomial identity, whereas whether or not a unit loop ...

In the present paper we generalize the concept of groups with triality and apply it to the theory of the Moufang, Bol and Bruck loops. Such generalizations allow us to reduce certain problems from the loop theory to problems ...

We describe the structure of a free loop of rank n in the variety of automorphic Moufang loops as a subdirect product of a free group and a free commutative Moufang loop, both of rank n. In particular, the variety of ...

We classify all unital subalgebras of the Cayley algebra O(q) over the finite field F(q), q = p(n). We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to ...