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A solution of a problem of Plotkin and Vovsi and an application to varieties of groups
Published online by Cambridge University Press: 09 April 2009
Abstract
Let K be an arbitrary field of characteristic 2, F a free group of countably infinite rank. We construct a finitely generated fully invariant subgroup U in F such that the relatively free group F/U satisfies the maximal condition on fully invariant subgroups but the group algebra K (F/U) does not satisfy the maximal condition on fully invariant ideals. This solves a problem posed by Plotkin and Vovsi. Using the developed techniques we also construct the first example of a non-finitely based (nilpotent of class 2)-by-(nilpotent of class 2) variety whose Abelian-by-(nilpotent of class at most 2) groups form a hereditarily finitely based subvariety.
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- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 67 , Issue 3 , December 1999 , pp. 329 - 355
- Copyright
- Copyright © Australian Mathematical Society 1999
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