10 citations · 38 across the 20 of their papers we have counts for
17 papers · 1 filter
The group identification problem for -groups of small order
Bettina Eick, Henrik Schanze
We investigate which group-theoretic invariants are powerful in distinguishing among non-isomorphic p-groups. Based on this, we devise an effective algorithm to solve the group ide…
Torsion-free nilpotent groups of small Hirsch length with isomorphic finite quotients
Alexander Cant, Bettina Eick
Let denote the class of finitely generated torsion-free nilpotent groups. For a group let be the set of isomorphism classes of finite quotients of . Pic…
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…
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…
Computing the order and the index of a subgroup in a polycyclic group
Bettina Eick
This contains a new version of the so-called non-commutative Gauss algorithm for polycyclic groups. Its results allow to read off the order and the index of a subgroup in an (possi…
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…