Groups satisfying the weak minimal condition

D. I. Zaitsev

doi:10.1007/bf01085210

Groups satisfying the weak minimal condition

Ukrainian Mathematical Journal ◽

10.1007/bf01085210 ◽

1969 ◽

Vol 20 (4) ◽

pp. 408-416 ◽

Cited By ~ 4

Author(s):

D. I. Zaitsev

Keyword(s):

Minimal Condition ◽

Weak Minimal Condition

Groups with the weak minimal condition on non-normal non-abelian subgroups

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry ◽

10.1007/s13366-019-00450-1 ◽

2019 ◽

Vol 61 (1) ◽

pp. 1-7 ◽

Cited By ~ 3

Author(s):

Fausto De Mari

Keyword(s):

Minimal Condition ◽

Weak Minimal Condition ◽

Abelian Subgroups

Groups With the Weak Minimal Condition on Non-Permutable Subgroups

Infinite Group Theory ◽

10.1142/9789813204058_0001 ◽

2017 ◽

pp. 1-18 ◽

Cited By ~ 1

Author(s):

Laxmi K. Chataut ◽

Martyn R. Dixon

Keyword(s):

Minimal Condition ◽

Weak Minimal Condition ◽

Permutable Subgroups

Weak minimal condition for nonnilpotent subgroups

Algebra and Logic ◽

10.1007/bf02071791 ◽

1984 ◽

Vol 23 (4) ◽

pp. 303-306 ◽

Cited By ~ 2

Author(s):

A. N. Ostylovskii

Keyword(s):

Minimal Condition ◽

Weak Minimal Condition

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

Ukrainian Mathematical Journal ◽

10.1007/bf01059601 ◽

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

Journal of Algebra ◽

10.1016/j.jalgebra.2020.04.034 ◽

2020 ◽

Vol 560 ◽

pp. 371-382

Author(s):

Ulderico Dardano ◽

Fausto De Mari ◽

Silvana Rinauro

Keyword(s):

Minimal Condition ◽

Normal Subgroups ◽

Weak Minimal Condition

ON GROUPS SATISFYING A WEAK MINIMAL CONDITION

Mathematics of the USSR-Sbornik ◽

10.1070/sm1969v007n03abeh001090 ◽

1969 ◽

Vol 7 (3) ◽

pp. 315-322 ◽

Cited By ~ 2

Author(s):

D I Zaĭcev

Keyword(s):

Minimal Condition ◽

Weak Minimal Condition

Groups satisfying the weak minimal condition for non-abelian subgroups

Ukrainian Mathematical Journal ◽

10.1007/bf01091653 ◽

1972 ◽

Vol 23 (5) ◽

pp. 543-546

Author(s):

D. I. Zaitsev

Keyword(s):

Minimal Condition ◽

Weak Minimal Condition ◽

Abelian Subgroups

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

Journal of Algebra ◽

10.1006/jabr.2001.9072 ◽

2002 ◽

Vol 249 (1) ◽

pp. 226-246 ◽

Cited By ~ 2

Author(s):

Martyn R. Dixon ◽

Martin J. Evans ◽

Howard Smith

Keyword(s):

Finite Groups ◽

Minimal Condition ◽

Weak Minimal Condition

Lie algebras satisfying the weak minimal condition on ideals

Hiroshima Mathematical Journal ◽

10.32917/hmj/1206130537 ◽

1986 ◽

Vol 16 (1) ◽

pp. 51-75

Author(s):

Takanori Sakamoto

Keyword(s):

Lie Algebras ◽

Minimal Condition ◽

Weak Minimal Condition

Groups with small deviation for non-subnormal subgroups

Open Mathematics ◽

10.2478/s11533-009-0012-9 ◽

2009 ◽

Vol 7 (2) ◽

Cited By ~ 1

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.