On lattices of radicals in the class of all finite groups

Authors

  • Jan Krempa Institute of Mathematics University of Warsaw
  • Izabela Agata Malinowska Institute of Mathematics University of Bialystok

Keywords:

finite groups, radicals, hereditary radicals, simple groups, lattices of radicals, balancdd lattices

Abstract

Lattices of radicals were extensively studied, for example, in the class of associative rings and led to some interesting results. In this paper we investigate the lattice L of all radicals in the class of all finite groups. We will also consider some its important sublattices. In particular, we prove that the lattice L is closed to being modular, the lattice L_h of all hereditary radicals is a Boolean algebra, and there exists a natural, useful projection of the lattice L onto L_h. 10.1017/S0004972712000056

Published

2012-10-22

Issue

Vol. 86 No. 3 (2012)

Section

Articles
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