Groups with the weak minimal condition for non-subnormal subgroups

1997 ◽  
Vol 173 (1) ◽  
pp. 299-312 ◽  
Author(s):  
Leonid A. Kurdachenko ◽  
Howard Smith
Keyword(s):  
Minimal Condition ◽  
Weak Minimal Condition ◽  
Subnormal Subgroups

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.

Groups With the Weak Minimal Condition on Non-Permutable Subgroups

2017 ◽  
pp. 1-18 ◽  
Author(s):  
Laxmi K. Chataut ◽  
Martyn R. Dixon
Keyword(s):  
Minimal Condition ◽  
Weak Minimal Condition ◽  
Permutable Subgroups

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

Two-step solvable groups with weak minimal condition for normal subgroups

1986 ◽  
Vol 37 (3) ◽  
pp. 232-236
Author(s):  
L. A. Kurdachenko ◽  
A. V. Tushev
Keyword(s):  
Solvable Groups ◽  
Minimal Condition ◽  
Normal Subgroups ◽  
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

Groups satisfying the weak minimal condition

1969 ◽  
Vol 20 (4) ◽  
pp. 408-416 ◽  
Author(s):  
D. I. Zaitsev
Keyword(s):  
Minimal Condition ◽  
Weak Minimal Condition

Groups Satisfying the Minimal Condition on Non-Subnormal Subgroups

1996 ◽  
Author(s):  
Silvana Franciosi ◽  
Francesco de Giovanni
Keyword(s):  
Minimal Condition ◽  
Subnormal Subgroups

ON GROUPS SATISFYING A WEAK MINIMAL CONDITION

1969 ◽  
Vol 7 (3) ◽  
pp. 315-322 ◽  
Author(s):  
D I Zaĭcev
Keyword(s):  
Minimal Condition ◽  
Weak Minimal Condition

Groups satisfying the weak minimal condition for non-abelian subgroups

1972 ◽  
Vol 23 (5) ◽  
pp. 543-546
Author(s):  
D. I. Zaitsev
Keyword(s):  
Minimal Condition ◽  
Weak Minimal Condition ◽  
Abelian Subgroups
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