Groups with small deviation for non-subnormal subgroups

Leonid Kurdachenko; Howard Smith

Open Mathematics (2009)

  • Volume: 7, Issue: 2, page 186-199
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Leonid Kurdachenko, and Howard Smith. "Groups with small deviation for non-subnormal subgroups." Open Mathematics 7.2 (2009): 186-199. <http://eudml.org/doc/269190>.

@article{LeonidKurdachenko2009,
abstract = {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.},
author = {Leonid Kurdachenko, Howard Smith},
journal = {Open Mathematics},
keywords = {Non-subnormal subgroups; Small deviation; non-subnormal subgroups; small deviation; non-subnormal deviation of groups; minimal condition; locally nilpotent groups; soluble groups},
language = {eng},
number = {2},
pages = {186-199},
title = {Groups with small deviation for non-subnormal subgroups},
url = {http://eudml.org/doc/269190},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Leonid Kurdachenko
AU - Howard Smith
TI - Groups with small deviation for non-subnormal subgroups
JO - Open Mathematics
PY - 2009
VL - 7
IS - 2
SP - 186
EP - 199
AB - 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.
LA - eng
KW - Non-subnormal subgroups; Small deviation; non-subnormal subgroups; small deviation; non-subnormal deviation of groups; minimal condition; locally nilpotent groups; soluble groups
UR - http://eudml.org/doc/269190
ER -

References

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