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A Boolean algebra of characteristic subgroups of a finite group

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Abstract

We construct a “natural” sublattice L(G) of the lattice of all of those subgroups of a finite group G that contain the Frattini subgroup \({\Phi(G)}\) . We show that L(G) is a Boolean algebra, and that its members are characteristic subgroups of G. If \({\Phi(G)}\) is trivial, then L(G) is exactly the set of direct factors U of G such that U and G/U have no common nontrivial homomorphic image.

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Authors and Affiliations

  1. Department of Mathematics, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait

    M. Deaconescu

  2. Department of Mathematics, University of Wisconsin, 480 Lincoln Dr., Madison, WI, 53706, USA

    I. M. Isaacs

  3. Department of Mathematics, Southeastern Louisiana University, Hammond, LA, 70403, USA

    G. L. Walls

Authors
  1. M. Deaconescu
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  2. I. M. Isaacs
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  3. G. L. Walls
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Correspondence to I. M. Isaacs.

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Deaconescu, M., Isaacs, I.M. & Walls, G.L. A Boolean algebra of characteristic subgroups of a finite group. Arch. Math. 97, 17–24 (2011). https://doi.org/10.1007/s00013-011-0283-9

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  • DOI: https://doi.org/10.1007/s00013-011-0283-9

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