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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.