The 3-closure of a solvable permutation group is solvable
نویسندگان
چکیده
Let m be a positive integer and let ? finite set. The m-closure of G?Sym(?) is the largest permutation group on having same orbits as G in its induced action Cartesian product ?m. 1-closure 2-closure solvable need not solvable. We prove that always for m?3.
منابع مشابه
Solvable $L$-subgroup of an $L$-group
In this paper, we study the notion of solvable $L$-subgroup of an $L$-group and provide its level subset characterization and this justifies the suitability of this extension. Throughout this work, we have used normality of an $L$-subgroup of an $L$-group in the sense of Wu rather than Liu.
متن کاملA Solvable Group Isospectral to S4(3)
We construct a solvable group G of order 5 648 590 729 620 such that the set of element orders of G coincides with that of the simple group S4(3). This completes the determination of finite simple groups isospectral to solvable groups.
متن کاملOn solvable minimally transitive permutation groups
We investigate properties of finite transitive permutation groups (G, Ω) in which all proper subgroups of G act intransitively on Ω. In particular, we are interested in reduction theorems for minimally transitive representations of solvable groups.
متن کاملExpanding Generator Sets for Solvable Permutation Groups
Let G = 〈S〉 be a solvable permutation group given as input by the generating set S. I.e. G is a solvable subgroup of the symmetric group Sn. We give a deterministic polynomial-time algorithm that computes an expanding generating set of size Õ(n2) for G. More precisely, given a λ < 1, we can compute a subset T ⊂ G of size Õ(n2) ( 1 λ )O(1) such that the undirected Cayley graph Cay(G,T ) is a λ-s...
متن کاملsolvable $l$-subgroup of an $l$-group
in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2022
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2021.07.002