scholarly journals Computing the composition factors of a permutation group in polynomial time

COMBINATORICA ◽  
1987 ◽  
Vol 7 (1) ◽  
pp. 87-99 ◽  
Author(s):  
Eugene M. Luks
Keyword(s):  
Permutation Group ◽  
Polynomial Time ◽  
Composition Factors

Permutation groups and orbits on the power set

2019 ◽  
Vol 19 (12) ◽  
pp. 2150005
Author(s):  
Yong Yang
Keyword(s):  
Permutation Group ◽  
Permutation Groups ◽  
Power Set ◽  
Composition Factors

Let [Formula: see text] be a permutation group of degree [Formula: see text] and let [Formula: see text] denote the number of set-orbits of [Formula: see text]. We determine [Formula: see text] over all groups [Formula: see text] that satisfy certain restrictions on composition factors.

Finding a cycle base of a permutation group in polynomial time

2018 ◽  
Vol 510 ◽  
pp. 542-561
Author(s):  
Mikhail Muzychuk ◽  
Ilia Ponomarenko
Keyword(s):  
Permutation Group ◽  
Polynomial Time

scholarly journals Polynomial-time normalizers

2011 ◽  
Vol Vol. 13 no. 4 ◽  
Author(s):  
Eugene M. Luks ◽  
Takunari Miyazaki
Keyword(s):  
Polynomial Time ◽  
Graph Isomorphism ◽  
Extensive Study ◽  
Permutation Groups ◽  
Linear Representations ◽  
Algorithms And Complexity ◽  
International Audience ◽  
Open Issue ◽  
Composition Factors ◽  
New Procedures

special issue in honor of Laci Babai's 60th birthday: Combinatorics, Groups, Algorithms, and Complexity International audience For an integer constant d \textgreater 0, let Gamma(d) denote the class of finite groups all of whose nonabelian composition factors lie in S-d; in particular, Gamma(d) includes all solvable groups. Motivated by applications to graph-isomorphism testing, there has been extensive study of the complexity of computation for permutation groups in this class. In particular, the problems of finding set stabilizers, intersections and centralizers have all been shown to be polynomial-time computable. A notable open issue for the class Gamma(d) has been the question of whether normalizers can be found in polynomial time. We resolve this question in the affirmative. We prove that, given permutation groups G, H \textless= Sym(Omega) such that G is an element of Gamma(d), the normalizer of H in G can be found in polynomial time. Among other new procedures, our method includes a key subroutine to solve the problem of finding stabilizers of subspaces in linear representations of permutation groups in Gamma(d).

scholarly journals Two-closure of odd permutation group in polynomial time

2001 ◽  
Vol 235 (1-3) ◽  
pp. 221-232 ◽  
Author(s):  
Sergei Evdokimov ◽  
Ilia Ponomarenko
Keyword(s):  
Permutation Group ◽  
Polynomial Time

scholarly journals Subgroups of minimal index in polynomial time

2019 ◽  
Vol 19 (01) ◽  
pp. 2050010
Author(s):  
Saveliy V. Skresanov
Keyword(s):  
Permutation Group ◽  
Polynomial Time ◽  
Proper Subgroup ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Cayley Table ◽  
Finite Permutation Group ◽  
Minimal Index

By applying an old result of Y. Berkovich, we provide a polynomial-time algorithm for computing the minimal possible index of a proper subgroup of a finite permutation group [Formula: see text]. Moreover, we find that subgroup explicitly and within the same time if [Formula: see text] is given by a Cayley table. As a corollary, we get an algorithm for testing whether or not a finite permutation group acts on a tree non-trivially.

scholarly journals Constructing composition factors for a linear group in polynomial time

2020 ◽  
Vol 561 ◽  
pp. 215-236
Author(s):  
Derek Holt ◽  
C.R. Leedham-Green ◽  
E.A. O'Brien
Keyword(s):  
Linear Group ◽  
Polynomial Time ◽  
Composition Factors

The 2-closure of a 32-transitive group in polynomial time

2018 ◽  
Vol 60 (2) ◽  
pp. 360-375
Author(s):  
A. V. Vasil'ev ◽  
D. V. Churikov
Keyword(s):  
Polynomial Time ◽  
Transitive Group
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