## An uncountable family of almost nilpotent varieties of polynomial growth.(English)Zbl 1431.16019

Summary: A non-nilpotent variety of algebras is almost nilpotent if any proper subvariety is nilpotent. Let the base field be of characteristic zero. It has been shown that for associative or Lie algebras only one such variety exists. Here we present infinite families of such varieties. More precisely we shall prove the existence of
1) a countable family of almost nilpotent varieties of at most linear growth and
2) an uncountable family of almost nilpotent varieties of at most quadratic growth.

### MSC:

 16P90 Growth rate, Gelfand-Kirillov dimension 16R10 $$T$$-ideals, identities, varieties of associative rings and algebras 17A50 Free nonassociative algebras 20C30 Representations of finite symmetric groups
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### References:

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