11 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…
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…