Sylow's theorem for Moufang loops

For finite Moufang loops, we prove an analog of the first Sylow theorem giving a criterion of 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 subloops.Comment: 21 page

Lie properties of crossed products

Let $F^\lambda_{\sigma} [G]$ be a crossed product of a group $G$ and the field $F$. We study the Lie properties of $F^\lambda_{\sigma} [G]$ in order to obtain a characterization of those crossed products which are upper (lower) Lie nilpotent and Lie $(n,m)$-Engel.Comment: 14 page

Filtered multiplicative bases of restricted enveloping algebras

We study the problem of the existence of filtered multiplicative bases of a restricted enveloping algebra u(L), where L is a finite-dimensional and p-nilpotent restricted Lie algebra over a field of positive characteristic p

ON SOME GENERALIZATIONS OF GROUPS WITH TRIALITY

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 in the theory of groups.CAPES (Brazil)CAPES (Brazil)FAPESP (Brazil)FAPESP (Brazil)CNPq (Brazil)CNPq (Brazil)RFFI (Russia)RFFI (Russia) [07-01-00392A, 10.01.00383A