The Number of Primitive Elements of the First and Second Degree of Free Non-associative Algebras over the Finite Field

A. A. Chepovskiy

M. V. Lomonosov Moscow State University

Abstract: Let $F_q$ be a finite field, $X=\{x_1,\ldots,x_n\}$ a set of free generators. Criteria for an element of the free non-associative algebra $F_q(X)$ to be primitive is obtained. Let $l$ be the degree of a primitive element. The number of primitive elements for $n = 1, 2$ and $l = 1, 2$ is found.

Keywords: free non-associative algebras, automorphisms of free algebras.

UDC: 512.554

Received: 05.03.2011