Related papers: A fast isomorphism test for groups of genus 2

We show that the problem to decide whether two (convex) polytopes, given by their vertex-facet incidences, are combinatorially isomorphic is graph isomorphism complete, even for simple or simplicial polytopes. On the other hand, we give a…

We present a new algorithm for constructive recognition of the Suzuki groups in their natural representations. The algorithm runs in Las Vegas polynomial time given a discrete logarithm oracle. An implementation is available in the Magma…

It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…

We present a deterministic polynomial-time algorithm that determines whether a finite module over a finite commutative ring is cyclic, and if it is, outputs a generator.

We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particular, we provide a practical algorithm to test nilpotency of…

We survey group-theoretic algorithms for finding (some or all) subgroups of a finite group and discuss the implementation of these algorithms in the computer algebra system GAP

We present a method for computing the number of epimorphisms from a finitely-presented group G to a finite solvable group \Gamma, which generalizes a formula of G\"aschutz. Key to this approach are the degree 1 and 2 cohomology groups of G,…

Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…

We obtain a classification of the finite two-generated cyclic-by-abelian groups of prime-power order. For that we associate to each such group $G$ a list $\inv(G)$ of numerical group invariants which determines the isomorphism type of $G$.…

In this paper we investigate the computational complexity of deciding if a given finite algebraic structure satisfies a fixed (strong) Maltsev condition $\Sigma$. Our goal in this paper is to show that $\Sigma$-testing can be accomplished…

We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.

We propose a new efficient algorithm for detecting if a cycle in a timed automaton can be iterated infinitely often. Existing methods for this problem have a complexity which is exponential in the number of clocks. Our method is polynomial:…

We study the codegree isomorphism problem for finite simple groups. In particular, we show that such a group is determined by the codegrees (counting multiplicity) of its irreducible characters. The proof is uniform for all simple groups…

We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.

The isomorphism problem for infinite finitely presented groups is probably the hardest among standard algorithmic problems in group theory. Classes of groups where it has been completely solved are nilpotent groups, hyperbolic groups, and…

We consider two basic algorithmic problems concerning tuples of (skew-)symmetric matrices. The first problem asks to decide, given two tuples of (skew-)symmetric matrices $(B_1, \dots, B_m)$ and $(C_1, \dots, C_m)$, whether there exists an…

We present the ideas behind an algorithm to compute normalizers of primitive groups with non-regular socle in polynomial time. We highlight a concept we developed called permutation morphisms and present timings for a partial implementation…

We show a polynomial-time algorithm for testing c-planarity of embedded flat clustered graphs with at most two vertices per cluster on each face.

Using the computational algebra system GAP (http://www.gap-system.org) and the GAP package LAGUNA (http://www.cs.st-andrews.ac.uk/~alexk/laguna.htm), we checked that all 2-groups of order not greater than 32 are determined by normalized…

The isomorphism problem means to decide if two given finite-dimensional simple algebras over the same centre are isomorphic and, if so, to construct an isomorphism between them. A solution to this problem has applications in computational…