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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 such that for every $n\in \ourset$ we can decide in time 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…