Infinite Periodic Words and Almost Nilpotent Varieties / *S. P. Mishchenko.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2017. № 4. P. 62-66
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 173-176].

An almost nilpotent variety of linear growth is constructed in the paper for any infinite periodic word in an alphabet of two letters. A discrete series of different almost nilpotent varieties is also constructed. Only a few almost nilpotent varieties were studied previously and their existence was proved often under some additional assumptions. The existence of almost nilpotent varieties of arbitrary integer exponential growth with a fractional exponent is proved as well as the existence of a continual family of almost nilpotent varieties with not more than quadratic growth.

*Key words*:
variety of linear algebras, identity, nilpotency, growth of the codimensions.