The structure of the commutative Moufang loops (CML) with minimum condition for subloops is examined. In particular it is proved that such a CML Q is a finite extension of a direct product of a finite number of the quasicyclic groups, lying in the centre of the CML Q. It is shown that the minimum conditions for subloops and for normal subloops are equivalent in a CML. Moreover, such CML also ch...

We proceed with Kunen's research about existence of units (left, right, two-sided) in quasigroups classical Bol--Moufang type identities, listed paper Extra loops II, by F. Fenyves (1969). consider those identities where it has not been decided yet whether a quasigroup fulfilling this identity to possess left or right identity. also provide table all Moufang--Bol indicating at each describes th...

In this paper, we consider some connections between loops whose loop rings, in characteristic 2, satisfy the Moufang identities and loops whose loop rings, in characteristic 2, satisfy the right Bol identities.

An extensive study of Moufang loops is given in [2].1 One defect of that study is that it assumes Moufang's associativity theorem [6], the only published proof of which involves a complicated induction. Using pseudo-automorphisms along with recent methods of Kleinfeld and the author [S], we shall give simple noninductive proofs of three associativity theorems, one of which (Theorem 5.1) general...