Category of groups

In mathematics, the category Grp (or Gp) has the class of all groups for objects and group homomorphisms for morphisms. As such, it is a concrete category. The study of this category is known as group theory.

Algebraic structure → Group theory
Group theory
Basic notions
  • Subgroup
  • Normal subgroup
Group homomorphisms
Finite groups
  • Schur multiplier
Classification of finite simple groups
Modular groups
  • PSL(2, )
  • SL(2, )
Topological and Lie groups
  • Special linear SL(n)
  • Orthogonal O(n)
  • Special orthogonal SO(n)
  • Unitary U(n)
  • Special unitary SU(n)
  • Symplectic Sp(n)
Infinite dimensional Lie group
  • O(∞)
  • SU(∞)
  • Sp(∞)
Algebraic groups
  • Linear algebraic group
  • Reductive group
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