# Bases of primitive linear groups II

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

SHOWING 1-4 OF 4 REFERENCES

A base of a permutation group G is a sequence B of points from the permutation domain such that only the identity of G fixes B pointwise. Answering a question of Pyber, we prove that all primitive
(1.1) Definition Let 1 6= G be a group. A subgroup M of G is said to be maximal if M 6= G and there exists no subgroup H such that M < H < G. IfG is finite, by order reasons every subgroupH 6= G is