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The Structure of Groups of Prime Power Order
1. Preliminaries 2. New groups from old 3. p-groups of maximal class 4. Finite p-groups acting uniserially 5. Lie Methods 6. The proof of Conjecture A 7. Pro-p-groups 8. Constructing finite p-groupsExpand
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
Linear Pro-p-Groups of Finite Width
Elementary properties of width.- p-adically simple groups .- Periodicity.- Chevalley groups.- Some classical groups.- Some thin groups.- Algorithms on fields.- Fields of small degree.- Algorithm forExpand
On the classification of prime-power groups by coclass
By giving a constructive proof of Conjecture P of Newman and O’Brien, we reduce the classification of certain p-groups of coclass r to a finite calculation. For the case p=2 we show that all 2-groupsExpand
The computational matrix group project
The Structure of Finite p‐Groups
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
Recognising tensor-induced matrix groups
Abstract We present an algorithm to decide whether or not a matrix group defined over a finite field is tensor-induced.