# The order of algebras with nontrivial fixed point subalgebras

## (*Lobachevskii Journal of Mathematics, Volume XXV*)

The paper represents an advancement of research the fundamental
problem of which is a classification of algebras *A* (Weil algebras
primarily) having a nontrivial fixed point subalgebra (with
respect to \underlineall algebra automorphisms). The main result
is the determination of the algebra order allowing a nontrivial
fixed point subalgebra. Moreover, an autonomous importance of some
results about socle elements of *A* and the unipotency of
algebra automorphisms is highlighted.