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Finiteness conditions in soluble groups and Lie algebras

  • Ian N. Stewart (a1)
Abstract

We prove some new theorems and reprove some old ones about finitely generated soluble groups and Lie algebras by a uniform method. Among the applications are Gruenberg's Theorem on Engel groups, for which we obtain a very short proof; and the Milnor and Wolf polynomial growth theorem. It is shown that a finitely generated soluble group with all 2-generator subgroups polycyclic is itself polycyclic, and that a finitely generated soluble Lie algebra, all of whose inner derivations are algebraic, is finite-dimensional. This last result enables us to give a partial answer to a question of Jacobson.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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