Groups with minimal conditions

Chernikov, N. S.

doi:10.1007/s10958-009-9715-5

Search citation statements

Order By: Relevance

Paper Sections

Select...

Proofs Of the Main Results2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2015

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(2 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let η be minimal among all ordinals ι, for which L ι includes such G. In view of Theorem B [12], η > 0. It is easy to see: for some ordinal λ, η = λ + 1.…”

Section: Proofs Of the Main Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Some Minimal Conditions in Certain Extremely Large Classes of Groups

Chernikov¹

2015

J. Sib. Fed. Univ., Math. phys.

View full text Add to dashboard Cite

Let L (respectively T) be the minimal local in the sense of D. Robinson class of groups, containing the class of weakly graded (respectively primitive graded) groups and closed with respect to forming subgroups and series. In the present paper, we completely describe: the L-groups with the minimal conditions for non-abelian subgroups and for non-abelian non-normal subgroups; the T-groups with the minimal conditions for (all) subgroups and for non-normal subgroups. By the way, we establish that every IHgroup, belonging to L, is solvable.

show abstract

“…Let η be minimal among all ordinals ι, for which L ι includes such G. In view of Theorem B [12], η > 0. It is easy to see: for some ordinal λ, η = λ + 1.…”

Section: Proofs Of the Main Resultsmentioning

confidence: 99%

“…Suppose that there exist Artinian non-Chernikov groups G ∈ T. Let η be minimal among all ordinal ι, for which L ι includes such G. Every Artinian primitive graded group is periodic and, at the same time, weakly graded. In view of Theorem B [12], Artinian weakly graded groups are Chernikov. Thus, η > 0.…”

Section: Proofs Of the Main Resultsmentioning

confidence: 99%

Some Minimal Conditions in Certain Extremely Large Classes of Groups

Chernikov¹

2015

J. Sib. Fed. Univ., Math. phys.

View full text Add to dashboard Cite

show abstract

Groups with minimal conditions

Cited by 1 publication

References 11 publications

Some Minimal Conditions in Certain Extremely Large Classes of Groups

Some Minimal Conditions in Certain Extremely Large Classes of Groups

Contact Info

Product

Resources

About