Weak minimal condition for nonnilpotent subgroups

1984 ◽  
Vol 23 (4) ◽  
pp. 303-306 ◽  
Author(s):  
A. N. Ostylovskii
Keyword(s):  
Minimal Condition ◽  
Weak Minimal Condition

The weak minimal condition on subgroups which fail to be close to normal subgroups

2020 ◽  
Vol 560 ◽  
pp. 371-382
Author(s):  
Ulderico Dardano ◽  
Fausto De Mari ◽  
Silvana Rinauro
Keyword(s):  
Minimal Condition ◽  
Normal Subgroups ◽  
Weak Minimal Condition

scholarly journals Locally Soluble-by-Finite Groups with the Weak Minimal Condition on Non-Nilpotent Subgroups

2002 ◽  
Vol 249 (1) ◽  
pp. 226-246 ◽  
Author(s):  
Martyn R. Dixon ◽  
Martin J. Evans ◽  
Howard Smith
Keyword(s):  
Finite Groups ◽  
Minimal Condition ◽  
Weak Minimal Condition

Groups with small deviation for non-subnormal subgroups

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Leonid Kurdachenko ◽  
Howard Smith
Keyword(s):  
Small Deviation ◽  
Minimal Condition ◽  
Baer Group ◽  
Weak Minimal Condition ◽  
Locally Nilpotent ◽  
Torsion Free ◽  
Subnormal Subgroups

AbstractWe 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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