Groups

When to Use

Use this skill when working on groups problems in abstract algebra.

Decision Tree

1. *Is G a group under operation ?

   • Check closure: a,b in G implies a*b in G?
   • Check associativity: (ab)c = a(bc)?
   • Check identity: exists e such that ea = ae = a?
   • Check inverses: for all a exists a^(-1) such that a*a^(-1) = e?
   • Verify with z3_solve.py prove "group_axioms"

2. Subgroup Test

   • Show H is non-empty (usually by showing e in H)
   • Show that for all a, b in H: ab^(-1) in H