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.

Details

Title
Groups with small deviation for non-subnormal subgroups
Author
Kurdachenko, Leonid 1 ; Smith, Howard 2 

 Algebra Department, Dnepropetrovsk University, Dnepropetrovsk, Ukraine 
 Department of Mathematics, Bucknell University, Lewisburg, USA 
Pages
186-199
Publication year
2009
Publication date
2009
Publisher
De Gruyter Poland
ISSN
18951074
e-ISSN
16443616
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2545258844
Copyright
© 2009. This work is published under http://creativecommons.org/licenses/by-nc-nd/3.0 (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.