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The p-Group Generation Algorithm
  • E. O'Brien
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • 1 May 1990
TLDR
The theory and implementation of an algorithm used in generating descriptions of p-groups aredescribed. Expand
Handbook of Computational Group Theory
History of Computational Group Theory BACKGROUND MATERIALS Fundamentals Group Actions Series Presentation of Groups Presentation of Subgroups Abelian Group Presentations Representation Theory,Expand
A Millennium Project: Constructing Small Groups
TLDR
We survey the problem of constructing the groups of a given finite order. Expand
Constructive recognition of classical groups in even characteristic
Abstract Let G = 〈 X 〉 ⩽ GL ( d , F ) be a classical group in its natural representation defined over a finite field F of even characteristic. We present Las Vegas algorithms to construct standardExpand
The Ore conjecture
The Ore conjecture, posed in 1951, states that every element of every finite non-abelian simple group is a commutator. Despite considerable effort, it remains open for various infinite families ofExpand
Generating random elements of a finite group
We present a "Practical" algorithm to construct random elements of a finite group. We analyse its theoretical behaviour and prove that asymptotically it produces uniformly distributed tuples ofExpand
CLASSIFYING 2-GROUPS BY COCLASS
Now that the conjectures of Leedham-Green and Newrnan have been proved, we probe deeper into the classification of p-groups using coclass. We determine the pro-2-groups of coclass at most 3 and useExpand
Enumerating classes and characters of p -groups
We develop general formulae for the numbers of conjugacy classes and irreducible complex characters of finite p-groups of nilpotency class less than p. This allows us to unify and generalize a numberExpand
Groups of deficiency zero
TLDR
In this paper we show how the use of symbolic computation changes the way in which one can attack previously intractable problems on group presentations. Expand
Isomorphism Testing for p-Groups
  • E. O'Brien
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • 1 February 1994
TLDR
We describe the theoretical and practical details of an algorithm which can be used to decide whether two given presentations for finite p-groups present isomorphic groups. Expand
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