The 3-closure of a solvable permutation group is solvable

The 3-closure of a solvable permutation group is solvable Full article

Journal

Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X

Output data

Year: 2022, Volume: 607, Pages: 618-637 Pages count : 20 DOI: 10.1016/j.jalgebra.2021.07.002

Tags

Finite groups; m-closure; Permutation groups

Authors

O'Brien E.A. ¹ , Ponomarenko I. ^2,3 , Vasil'ev A.V. ^3,4 , Vdovin E. ^3,4

Affiliations

1	Department of Mathematics, The University of Auckland, Auckland, New Zealand
2	Steklov Institute of Mathematics at St. Petersburg, Russia
3	Sobolev Institute of Mathematics, Novosibirsk, Russia
4	Novosibirsk State University, Novosibirsk, Russia

Funding (2)

1	Russian Foundation for Basic Research	18-01-00752
2	Министерство науки и высшего образования РФ Mathematical Center in Akademgorodok	075-15-2019-1613, 075-15-2022-281

Let m be a positive integer and let Ω be a finite set. The m-closure of G≤Sym(Ω) is the largest permutation group on Ω having the same orbits as G in its induced action on the Cartesian product Ωm. The 1-closure and 2-closure of a solvable permutation group need not be solvable. We prove that the m-closure of a solvable permutation group is always solvable for m≥3. © 2021 Elsevier Inc.

O'Brien E.A. , Ponomarenko I. , Vasil'ev A.V. , Vdovin E.
The 3-closure of a solvable permutation group is solvable
Journal of Algebra. 2022. V.607. P.618-637. DOI: 10.1016/j.jalgebra.2021.07.002 WOS Scopus РИНЦ OpenAlex

Submitted:	Jan 28, 2021
Published online:	Jul 13, 2021

Web of science:	WOS:000833526600024
Scopus:	2-s2.0-85110998304
Elibrary:	46943743
OpenAlex:	W3116258519

DB	Citing
Scopus	3
Web of science	3
OpenAlex	7
Elibrary	2