Computational Aspects of Finite p-Groups - Lecture 1

Explore computational aspects of finite p-groups in this 55-minute lecture from the Group Theory and Computational Methods program at the International Centre for Theoretical Sciences. Delve into the abundance and importance of p-groups, learn about group presentations and central series, and understand polycyclic groups and their sequences. Discover normal forms, polycyclic presentations, and the collection algorithm. Examine consistency checks and weighted power-commutator presentations as part of this comprehensive introduction to computational techniques in group theory.

Group Theory and Computational Methods
p-group - 1
Computational aspects of finite p-groups
Welcome! And a bit about myself...
Why p-groups?
There's an abundant supply of p-groups
Important aspects of p-groups
Outline of this lecture series
Main resources*
Groups and computers
Group presentations
Background: central series
Example: central series
Polycyclic groups
Polycyclic Sequence
Normal Forms
Example: Normal Forms
Polycyclic group to presentation
Pc presentation to group
Consistent pc presentations
Collection
Collection algorithm
Example: collection
Consistency checks
Weighted power-commutator presentation
Conclusion Lecture 1