Bases of primitive linear groups II

M. Liebeck

DOI:10.1016/j.jalgebra.2014.01.011
Corpus ID: 123051865

Bases of primitive linear groups II

@inproceedings{Liebeck2014BasesOP,
  title={Bases of primitive linear groups II},
  author={Martin W. Liebeck},
  year={2014}
}

M. Liebeck
Published 2014
Mathematics

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14 Citations

Highly Influential Citations

Background Citations

Methods Citations

Every coprime linear group admits a base of size two

Z. HalasiK. Podoski
Mathematics
2012

Let G be a linear group acting on the finite vector space V and assume that (|G|,|V|)=1. In this paper we prove that G has a base size at most two and this estimate is sharp. This generalizes and…

Bases of primitive permutation groups

Joanna B. Fawcett
Mathematics
2013

A base B for a finite permutation group G acting on a set Ω is a subset of Ω with the property that only the identity of G can fix every element of B. In this dissertation, we investigate some…

Abelian quotients and orbit sizes of solvable linear groups

T. KellerYong Yang
Mathematics
2016

Let G be a finite group, and let V be a completely reducible faithful Gmodule. It has been known for a long time that if G is abelian, then G has a regular orbit on V. In this paper we generalize…

Bases of twisted wreath products

Joanna B. Fawcett
Mathematics
Journal of Algebra
2021

P-schemes and Deterministic Polynomial Factoring Over Finite Fields

Zeyu Guo
Mathematics, Computer Science
2017

This work develops a unifying framework for the problem of deterministic factoring of univariate polynomials over finite field under the generalized Riemann hypothesis (GRH), and provides explicit constructions of strongly antisymmetric homogeneous m-schemes for m≤3.

P-schemes : a unifying framework for deterministic polynomial factoring over finite fields ( research summary )

Zeyu Guo
Mathematics, Computer Science
2017

A unifying framework for deterministic polynomial factoring over finite fields under the generalized Riemann hypothesis (GRH) is developed and it is proved that a polynopoly f(X) ∈ Fp[X] can be factorized in polyn coefficients time given an irreducible polynometric lifting f( X) whose Galois group is in Γk.

Bases for quasisimple linear groups

Melissa LeeM. Liebeck
Mathematics
Algebra & Number Theory
2018

Let $V$ be a vector space of dimension $d$ over $F_q$, a finite field of $q$ elements, and let $G \le GL(V) \cong GL_d(q)$ be a linear group. A base of $G$ is a set of vectors whose pointwise…

A Faster Isomorphism Test for Graphs of Small Degree

Martin GroheDaniel NeuenPascal Schweitzer
Mathematics
2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
2018

This work gives an improved isomorphism test for graphs of small degree: their algorithms runs in time n^O((log d)^c), where n is the number of vertices of the input graphs, d is the maximum degree of theinput graphs, and c is an absolute constant.

Towards faster isomorphism tests for bounded-degree graphs

Martin GroheDaniel NeuenPascal Schweitzer
Mathematics
ArXiv
2018

There is an n-isomorphism test for all classes of graphs of maximum degree d and diameter at most $O(\log n)$ and this implies that there is an $n^{\text{polylog}(d)}$- isomorphismTest for all families of $d$-regular expander graphs.

$\mathcal{P}$-schemes and Deterministic Polynomial Factoring over Finite Fields

Zeyu Guo
Mathematics, Computer Science
2017

A unifying framework for the problem of deterministic factoring of univariate polynomials over finite fields under the generalized Riemann hypothesis (GRH).

References

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