## 14 Citations

### Every coprime linear group admits a base of size two

- 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

- 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

- 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…

### P-schemes and Deterministic Polynomial Factoring Over Finite Fields

- 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 )

- 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

- MathematicsAlgebra & 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

- Mathematics2018 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

- MathematicsArXiv
- 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

- 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

### The Minimal Base Size of Primitive Solvable Permutation Groups

- Mathematics
- 1996

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…

### On the maximal subgroups of the finite classical groups

- Mathematics
- 1984

(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…