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Chebyshevskii Sb., 2018, Volume 19, Issue 1, Pages 176–186 (Mi cheb630)  

Variety with fractional codimension growth and the Specht problem

S. P. Mishchenkoa, O. V. Shulezhkob

a Ulyanovsk State University
b Ulyanovsk state pedagogical University named after I. N. Ulyanov

Abstract: According to A.I. Maltsev, a set of linear algebras in which a fixed set of identities is called a variety. Using the language of the theory of Lie algebras, we say that the algebra is metabelian if it satisfies the identity $(xy)(zt)\equiv 0 $. A variety is called Specht if it is such a variety and any of its subvariety has a finite basis of identities. Codimension growth is determined by sequence of dimensions multilinear parts of a relatively free algebra of a variety. This sequence is called a sequence codimensions, referring to the multilinear spaces of the ideal identities of the variety. This article presents the results related to the problem of fractional polynomial growth. The review gives new examples of such varieties, and also give a new example of a variety with an infinite basis of identities.

Keywords: identity, variety, codimension, metabelian, shpecht.

DOI: https://doi.org/10.22405/2226-8383-2018-19-1-176-186

Full text: PDF file (518 kB)
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UDC: 512.5

Citation: S. P. Mishchenko, O. V. Shulezhko, “Variety with fractional codimension growth and the Specht problem”, Chebyshevskii Sb., 19:1 (2018), 176–186

Citation in format AMSBIB
\Bibitem{MisShu18}
\by S.~P.~Mishchenko, O.~V.~Shulezhko
\paper Variety with fractional codimension growth
and the Specht problem
\jour Chebyshevskii Sb.
\yr 2018
\vol 19
\issue 1
\pages 176--186
\mathnet{http://mi.mathnet.ru/cheb630}
\crossref{https://doi.org/10.22405/2226-8383-2018-19-1-176-186}
\elib{https://elibrary.ru/item.asp?id=36312685}


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