Computational Techniques in Finite Group Theory: Python Implementations and Applications
Seddik Abdelalim
LMFA, FSAC, University Hassan II of Casablanca, Morocco.
Ilias Elmouki *
LMFA, FSAC, University Hassan II of Casablanca, Morocco.
Noreddine Abghour
LIS Labs, FSAC, University Hassan II of Casablanca, Morocco.
*Author to whom correspondence should be addressed.
Abstract
This study introduces algorithmic schemes in Python for computing some basic substructures of finite groups, namely subgroups cosets and generators, as well as some examples of cyclic groups. For this, paper provide 12 examples to motivate the reader to become familiar with programming on this topic.
Keywords: Cayley’s table, Abelian group, subgroup, generator, Lucas-Lehmer condition, Lagrange’s theorem, Cyclic group