Alexandrou, Maria and Stöhr, Ralph
(2014)
*Free centre-by-nilpotent-by-abelian Lie rings of rank 2.*
[MIMS Preprint]

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## Abstract

We study the free Lie ring of rank $2$ in the variety of all centre-by-nilpotent-by-abelian Lie rings of derived length $3$. This is the quotient $L/([\gamma_c(L'),L]+L''')$ with $c\geqslant 2$ where $L$ is the free Lie ring of rank $2$, $\gamma_c(L')$ is the $c$-th term of the lower central series of the derived ideal $L'$ of $L$, and $L'''$ is the third term of the derived series of $L$. We show that the quotient $\gamma_c(L')+L'''/[\gamma_c(L'),L]+L'''$ is a direct sum of a free abelian group and a torsion group of exponent $c$. We exhibit an explicit generating set for the torsion subgroup.

Item Type: | MIMS Preprint |
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Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebras |

Depositing User: | Prof Ralph Stöhr |

Date Deposited: | 25 Jul 2014 |

Last Modified: | 08 Nov 2017 18:18 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2158 |

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