Influence of minimal subgroups on the product of smooth groups

  • Abstract
  • Keywords
  • References
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  • Abstract

    A maximal chain in a finite lattice L is called smooth if any two intervals of the same length are isomorphic. We say that a finite group G is totally smooth if all maximal chains in its subgroup lattice L(G) are smooth. In this article, we study the product of finite groups which have a permutable subgroup of prime order under the assumption that the maximal subgroups are totally smooth.

  • Keywords

    Permutable subgroups; Smooth groups; Subgroup lattices.

  • References

      [1] A. M. Elkholy, "On totally smooth groups", Int. J. Algebra, Vol.1, No.2, (2007), pp.63-70.

      [2] K. Doerk, T. Hawkes, Finite soluble groups. Walter de Gruyter, Berlin-New York, (1992).

      [3] M. Asaad, Shaalan, "On the supersolvability of finite groups", Arch. Math, 53, (1989), pp.318-326.

      [4] R. Schmidt, "Smooth groups", Geometriae Dedicata, 84, (2001), pp.183-206.

      [5] R. Schmidt, "Smooth p-groups", J. Algebra, 234, (2000), pp.533-5390.

      [6] R. Schmidt, Subgroup lattices of groups. Walter de Gruyter, Berlin-New York, Berlin-New York, (1994).




Article ID: 4182
DOI: 10.14419/ijbas.v4i2.4182

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