Group Theory

Group Theory

1. Elementary Properties

   • Theorem: The identity element in a group is unique
   • Theorem: Every element in a group has a unique inverse
   • Sugroup
     • Definition : closure, identity, inverses denoted as H <= G
   • Power of Elements
   • Cyclic Subgroups

2. Group Isomorphisms

   • Two groups are isomorphic if and only if there exists a bijection
   • Properties: number of elements, subgroups are the same
   • f(a+b) = f(a) + f(b)

3. Field

   • Abelian group, distributive law holds