HUNTERTUTORING

Groups

Abstract algebra · Theoretical / proof-based

Binary operations, equivalence relations, and modular arithmetic

Objectives

  • Binary operations, equivalence relations, and modular arithmetic
  • Groups: definitions, examples (Z, Z_n, dihedral, symmetric groups)
  • Subgroups and cyclic groups; generators and order
  • Cosets, Lagrange's theorem, and index
  • Normal subgroups and quotient groups
  • Group homomorphisms and the first isomorphism theorem
  • Direct products and simple groups (introduction)

Study materials