Heiko Dietrich

activity

20122026

most citedGroups in which every non-abelian subgroup is self-centralizing

15 citations · 63 across the 18 of their papers we have counts for

collaborators

24 papers

math.GR2026

The number of groups of cubefree order

Heiko Dietrich, David Jefferies

Generalising Hölder's classical group enumeration for squarefree orders (1895), we provide an exact formula for the number of isomorphism types of groups of a given cubefree order.…

math.GR2026

The Monster group is a completion of the Goldschmidt G3-amalgam

Heiko Dietrich

We prove the claim in the title and complete Parker and Rowley's classification (J. Algebra 2001) of which sporadic simple groups are completions of the Goldschmidt G3-amalgam.

math.GR2023

The origins of Coclass Theory

Heiko Dietrich, Bettina Eick

In 1980, Leedham-Green and Newman introduced the invariant coclass to the theory of groups of prime-power order and they proposed five far-reaching conjectures related to it. Their…

math.GR2023★ 9 cited

The maximal subgroups of the Monster

Heiko Dietrich, Melissa Lee, Tomasz Popiel

The classification of the maximal subgroups of the Monster $M$ is a long-standing problem in finite group theory. According to the literature, the classification is comple…

math.GR2023

Elementary abelian subgroups: from algebraic groups to finite groups

Jianbei An, Heiko Dietrich, Alastair J. Litterick

We describe a new approach for classifying conjugacy classes of elementary abelian subgroups in simple algebraic groups over an algebraically closed field, and understanding the no…

math.GR2022

Derangements in wreath products of permutation groups

Vishnuram Arumugam, Heiko Dietrich, S. P. Glasby

Given a finite group $G$ acting on a set $X$ let $δ_{k} (G, X)$ denote the proportion of elements in $G$ that have exactly $k$ fixed points in $X$ . Let $S_{n}$ denote the symmet…

quant-ph2022

Classification of four-rebit states

Heiko Dietrich, Willem A. de Graaf, Alessio Marrani +1

We classify states of four rebits, that is, we classify the orbits of the group $G (R) = SL (2, R)^{4}$ in the space $(\mathbb R^2)^{\otimes…

quant-ph2021★ 7 cited

Classification of four qubit states and their stabilisers under SLOCC operations

Heiko Dietrich, Willem A. de Graaf, Alessio Marrani +1

We classify four qubit states under SLOCC operations, that is, we classify the orbits of the group $SL (2, C)^{4}$ on the Hilbert space $\mathcal{H}_4 = (\ma…

math.GR2021

The isomorphism problem for plain groups is in $Σ_{3}^{P}$

Heiko Dietrich, Murray Elder, Adam Piggott +2

Testing isomorphism of infinite groups is a classical topic, but from the complexity theory viewpoint, few results are known. S{é}nizergues and the fifth author (ICALP2018) proved…

math.GR2021

Galois trees in the graph of $p$ -groups of maximal class

Alexander Cant, Heiko Dietrich, Bettina Eick +1

The investigation of the graph $G_{p}$ associated with the finite $p$ -groups of maximal class was initiated by Blackburn (1958) and became a deep and interesting research t…

math.RT2021

A note on étale representations from nilpotent orbits

Heiko Dietrich, Wolfgang Globke, Marcos Origlia

A linear étale representation of a complex algebraic group $G$ is given by a complex algebraic $G$ -module $V$ such that $G$ has a Zariski-open orbit on $V$ and $dim G = dim V$ . A c…

math.GR2020★ 5 cited

Groups whose orders factorise into at most four primes

Heiko Dietrich, Bettina Eick, Xueyu Pan

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…

cs.CC2020

Group isomorphism is nearly-linear time for most orders

Heiko Dietrich, James B. Wilson

We show that there is a dense set $\ourset\subseteq \mathbb{N}$ of group orders and a constant $c$ such that for every $n\in \ourset$ we can decide in time $O (n^{2} (lo g n)^{c})$ wheth…

math.GR2020

Generation of finite groups with cyclic Sylow subgroups

Heiko Dietrich, Darren Low

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 grou…

math.GR2019★ 5 cited

Universal Covers of Finite Groups

Heiko Dietrich, Alexander Hulpke

Motivated by quotient algorithms, such as the well-known $p$ -quotient or solvable quotient algorithms, we describe how to compute extensions $H ~$ of a finite group $H$ by a d…

math.RT2019

Computing the real Weyl group

Heiko Dietrich, Willem A. de Graaf

Let g be a semisimple Lie algebra over the real numbers. We describe an explicit combinatorial construction of the real Weyl group of g with respect to a given Cartan subalgebra. A…

math.CO2019

Constructing cocyclic Hadamard matrices of order 4p

Santiago Barrera Acevedo, Heiko Dietrich, Padraig O Cathain

Cocyclic Hadamard matrices (CHMs) were introduced by de Launey and Horadam as a class of Hadamard matrices with interesting algebraic properties. Ó Catháin and Röder described a cl…

math.GR2019

On two group functors extending Schur multipliers

Heiko Dietrich, Primoz Moravec

Liedtke (2008) has introduced group functors $K$ and $K ~$ , which are used in the context of describing certain invariants for complex algebraic surfaces. He proved that these…

math.GR2018★ 7 cited

Isomorphism testing of groups of cube-free order

Heiko Dietrich, James B. Wilson

A group $G$ has cube-free order if no prime to the third power divides $∣ G ∣$ . We describe an algorithm that given two cube-free groups $G$ and $H$ of known order, decides whether $…

math.GR2018★ 4 cited

Polynomial-time isomorphism testing of groups of most finite orders

Heiko Dietrich, James B. Wilson

[PLEASE SEE COMMENT] We consider the isomorphism problem for finite abelian groups and finite meta-cyclic groups. We prove that for a dense set of positive integers $n$ , isomorphis…

math.GR2017★ 3 cited

Small partial Latin squares that embed in an infinite group but not into any finite group

Heiko Dietrich, Ian M. Wanless

Suppose that $Y_{1}, Y_{2}, Y_{3}$ are finite sets and $P \subseteq Y_{1} \times Y_{2} \times Y_{3}$ . We say that $P$ embeds in a group $G$ if there exist injective maps $ϕ_i\colon Y_i\rightarrow G…

math.RT2016★ 8 cited

Nilpotent orbits in real symmetric pairs and stationary black holes

Heiko Dietrich, Willem A. de Graaf, Daniele Ruggeri +1

In the classification of stationary solutions in extended supergravities with symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play an important role. In t…

math.GR2015★ 15 cited

Groups in which every non-abelian subgroup is self-centralizing

Costantino Delizia, Heiko Dietrich, Primoz Moravec +1

We study groups having the property that every non-abelian subgroup contains its centralizer. We describe various classes of infinite groups in this class, and address a problem of…

math.RA2012

A computational approach to the Kostant-Sekiguchi correspondence

Heiko Dietrich, Willem A. de Graaf

Let g be a real form of a simple complex Lie algebra. Based on ideas of Djokovic and Vinberg, we describe an algorithm to compute representatives of the nilpotent orbits of g using…

The number of groups of cubefree order

The Monster group is a completion of the Goldschmidt G3-amalgam

The origins of Coclass Theory

The maximal subgroups of the Monster

Elementary abelian subgroups: from algebraic groups to finite groups

Derangements in wreath products of permutation groups

Classification of four-rebit states

Classification of four qubit states and their stabilisers under SLOCC operations

The isomorphism problem for plain groups is in Σ3P​

Galois trees in the graph of p-groups of maximal class

A note on étale representations from nilpotent orbits

Groups whose orders factorise into at most four primes

Group isomorphism is nearly-linear time for most orders

Generation of finite groups with cyclic Sylow subgroups

Universal Covers of Finite Groups

Computing the real Weyl group

Constructing cocyclic Hadamard matrices of order 4p

On two group functors extending Schur multipliers

Isomorphism testing of groups of cube-free order

Polynomial-time isomorphism testing of groups of most finite orders

Small partial Latin squares that embed in an infinite group but not into any finite group

Nilpotent orbits in real symmetric pairs and stationary black holes

Groups in which every non-abelian subgroup is self-centralizing

A computational approach to the Kostant-Sekiguchi correspondence

The isomorphism problem for plain groups is in $Σ_{3}^{P}$

Galois trees in the graph of $p$ -groups of maximal class