Related papers: The construction of finite solvable groups revisit…
We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given finite metacyclic groups are isomorphic, and another algorithm…
We introduce a new constructive recognition algorithm for finite special linear groups in their natural representation. Given a group $G$ generated by a set of $d\times d$ matrices over a finite field $\mathbb{F}_q$, known to be isomorphic…
We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…
We study the realization problem of finite groups as the group of homotopy classes of self-homotopy equivalences of finite spaces. Let $G$ be a finite group. Using an infinite family of pairwise non weakly homotopic asymmetric spaces we…
This paper gives a systematic construction of certain covers of finite semigroups. These covers will be used in future work on the complexity of finite semigroups.
Slattery (2007) described computational methods to enumerate, construct, and identify finite groups of squarefree order. We generalise Slattery's result to the class of finite groups that have cyclic Sylow subgroups and provide an…
A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.
We develop a practical algorithm to decide whether a finitely generated subgroup of a solvable algebraic group $G$ is arithmetic. This incorporates a procedure to compute a generating set of an arithmetic subgroup of $G$. We also provide a…
In this paper we survey a new criteria for solvability of finite groups in terms of number of supersolvable (also known as polycyclic) and non-supersolvable subgroups. In particular, we present original examples of supersolvable groups such…
In this paper it is shown how to construct a finite topological space $X$ for a given finitely presentable group $G$ such that $\pi_1(X)\cong G$. Our construction is not optimal in the sense that the cardinality of the space $X$ might not…
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
A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. The method is illustrated by an example. We also discuss an implementation of the algorithm in the language of the…
The groups whose orders factorise into at most four primes have been described (up to isomorphism) in various papers. Given such an order n, this paper exhibits a new explicit and compact determination of the isomorphism types of the groups…
We introduce the isoclinism of crossed modules. We also give GAP implementations for constructing the isoclinism families of finite crossed modules and consequently give an enumeration about isoclinic crossed modules existing in the GAP…
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…
A finitely generated solvable group with unbounded iterated identity is constructed.
This is a collection of examples showing how the GAP system can be used to compute information about the probabilistic generation of finite almost simple groups. It includes all examples that were needed for the computational results in the…
In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising…
We prove that the isomorphism problem for finitely generated fully residually free groups is decidable. We also show that each finitely generated fully residually free group G has a decomposition that is invariant under automorphisms of G,…