On the length of a finite group and of its 2-generator subgroups

Detomi, Eloisa; Shumyatsky, Pavel

doi:10.1007/s00574-016-0191-5

Cited by 2 publications

(3 citation statements)

References 10 publications

(11 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also, H ′ is a cyclic extension of U n−1 (q), therefore H ∈ Λ 1 , whenever (n, q) = (3, 3). For S = U 3 (3), a direct inspection in [5] suggests that we may take H to be the maximal subgroup L 2 (7). iv.…”

Section: Proof Case S Alternatingmentioning

confidence: 99%

“…Therefore, as long as (n, q) ∈ {(3, 2), (3, 3)} the subgroup H lies in Λ 1 . Finally note that L 3 (2) ≃ L 2 (7) and L 3 (3) are minimal simple groups and so they belong to L.…”

Section: Proof Case S Alternatingmentioning

confidence: 99%

“…The minimum number of nonsolvable factors attained on all possible such series is called the nonsolvable length of G and denoted by λ(G) (see [11]). In a series of recent papers (see also [13], [12], [7], [3], [4]) this parameter has been investigated, as some bounds on λ(G) have been proved to be useful in several situations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A reduction theorem for nonsolvable finite groups

2019

View full text Add to dashboard Cite

Every finite group G has a normal series each of whose factors is either a solvable group or a direct product of nonabelian simple groups. The minimum number of nonsolvable factors attained on all possible such series is called the nonsolvable length of the group and denoted by λ(G). For every integer n, we define a particular class of groups of nonsolvable length n, called n-rarefied, and we show that every finite group of nonsolvable length n contains an n-rarefied subgroup. As applications of this result, we improve the known upper bounds on λ(G) and determine the maximum possible nonsolvable length for permutation groups and linear groups of fixed degree resp. dimension.

show abstract

Section: Proof Case S Alternatingmentioning

confidence: 99%

“…Therefore, as long as (n, q) ∈ {(3, 2), (3, 3)} the subgroup H lies in Λ 1 . Finally note that L 3 (2) ≃ L 2 (7) and L 3 (3) are minimal simple groups and so they belong to L.…”

Section: Proof Case S Alternatingmentioning

confidence: 99%

See 1 more Smart Citation

A reduction theorem for nonsolvable finite groups

2019

View full text Add to dashboard Cite

show abstract

On the Rank of a Verbal Subgroup of a Finite Group

Detomi¹,

Morigi

Shumyatsky³

2021

J. Aust. Math. Soc.

Self Cite

View full text Add to dashboard Cite

We show that if w is a multilinear commutator word and G a finite group in which every metanilpotent subgroup generated by w-values is of rank at most r, then the rank of the verbal subgroup $w(G)$ is bounded in terms of r and w only. In the case where G is soluble, we obtain a better result: if G is a finite soluble group in which every nilpotent subgroup generated by w-values is of rank at most r, then the rank of $w(G)$ is at most $r+1$ .

show abstract

On the length of a finite group and of its 2-generator subgroups

Abstract: The nonsoluble length λ(

Cited by 2 publications

References 10 publications

A reduction theorem for nonsolvable finite groups

A reduction theorem for nonsolvable finite groups

On the Rank of a Verbal Subgroup of a Finite Group

Contact Info

Product

Resources

About