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  • ON LATTICES OF RADICALS IN THE CLASS OF ALL FINITE GROUPS

  • Part of
  • JAN KREMPA, IZABELA AGATA MALINOWSKA
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 86 / Issue 3 / December 2012
    Published online by Cambridge University Press:
    16 February 2012, pp. 495-505
    Print publication:
    December 2012
    • Article
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  • Lattices of radicals have been extensively studied, for example in the class of associative rings, leading to some interesting results. In this paper we investigate the lattice L of all radicals in the class of all finite groups. We also consider some of its important sublattices. In particular, we prove that the lattice L is closed to being modular, the lattice Lh of all hereditary radicals is a Boolean algebra, and there exists a natural, useful projection of the lattice L onto Lh.