Introductory Essentials to Finite Abelian Groups
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 deals with the properties of finite abelian groups. We first start by stating the fundamental theorems such as those of Cayley, Lagrange, Poincar´e, and the three isomorphism theorems. Then, we move on to the first and second Sylow theorems. Finally, we discuss some applications of finite Abelian groups, and we include fifty exercises on this topic, some of which belong to the ”Agregation”.
Keywords: Finite Abelian groups, isomorphism theorems, group actions, Sylow theorems