Groups with small deviation for non-subnormal subgroups

Leonid Kurdachenko 1  and Howard Smith 2
  • 1 Algebra Department, Dnepropetrovsk University, Dnepropetrovsk, Ukraine
  • 2 Department of Mathematics, Bucknell University, Lewisburg, USA


We introduce the notion of the non-subnormal deviation of a group G. If the deviation is 0 then G satisfies the minimal condition for nonsubnormal subgroups, while if the deviation is at most 1 then G satisfies the so-called weak minimal condition for such subgroups (though the converse does not hold). Here we present some results on groups G that are either soluble or locally nilpotent and that have deviation at most 1. For example, a torsion-free locally nilpotent with deviation at most 1 is nilpotent, while a Baer group with deviation at most 1 has all of its subgroups subnormal.

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