15 citations · 63 across the 18 of their papers we have counts for
16 papers · 1 filter
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.…
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.
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…
The maximal subgroups of the Monster
Heiko Dietrich, Melissa Lee, Tomasz Popiel
The classification of the maximal subgroups of the Monster is a long-standing problem in finite group theory. According to the literature, the classification is comple…
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…
Derangements in wreath products of permutation groups
Vishnuram Arumugam, Heiko Dietrich, S. P. Glasby
Given a finite group acting on a set let denote the proportion of elements in that have exactly fixed points in . Let denote the symmet…
The isomorphism problem for plain groups is in
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…
Galois trees in the graph of -groups of maximal class
Alexander Cant, Heiko Dietrich, Bettina Eick +1
The investigation of the graph associated with the finite -groups of maximal class was initiated by Blackburn (1958) and became a deep and interesting research t…
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…
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…
Universal Covers of Finite Groups
Heiko Dietrich, Alexander Hulpke
Motivated by quotient algorithms, such as the well-known -quotient or solvable quotient algorithms, we describe how to compute extensions of a finite group by a d…
On two group functors extending Schur multipliers
Heiko Dietrich, Primoz Moravec
Liedtke (2008) has introduced group functors and , which are used in the context of describing certain invariants for complex algebraic surfaces. He proved that these…
Isomorphism testing of groups of cube-free order
Heiko Dietrich, James B. Wilson
A group has cube-free order if no prime to the third power divides . We describe an algorithm that given two cube-free groups and of known order, decides whether $…
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 , isomorphis…
Small partial Latin squares that embed in an infinite group but not into any finite group
Heiko Dietrich, Ian M. Wanless
Suppose that are finite sets and . We say that embeds in a group if there exist injective maps $ϕ_i\colon Y_i\rightarrow G…
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…