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1 results

  • 11 - Lattice-Theoretic Characterizations of Classes of Groups

  • Edited by Ron Donagi, University of Pennsylvania, Tony Shaska, Oakland University, Michigan
  • Book:
    Integrable Systems and Algebraic Geometry
    Published online:
    19 March 2020
    Print publication:
    02 March 2020, pp 367-382

  • Summary

    One of the most interesting problems in the field Subgroup Lattices of Groups is to find lattice-theoretic characterizations of interesting classes of groups. After explaining this problem by looking at the classical characterizations of cyclic and of finite soluble groups, we first present lattice-theoretic characterizations of some classes of infinite soluble groups. Then for a finite group G we try to determine in its subgroup lattice L(G) the Fitting length of G and properties defined by arithmetical conditions. For this we use some new ideas to determine minimal normal subgroups and the orders of minimal subgroups in L(G).