abelian group alternating group baby monster group character theory circle circle group classification of finite simple groups commutative ring conway group coprime coset cyclic module dihedral group direct product discrete group divisor endomorphism ring field extension finite field finitely generated abelian group fischer group fundamental theorem of cyclic groups galois group general linear group generating set of a group glossary of group theory greatest common divisor group homomorphism group isomorphism group theory hyperbolic group index calculus algorithm integer isomorphism janko group klein four-group lattice of subgroups lie group localization of a ring loop group lorentz group mathematical reviews mathieu group modular arithmetic modular group modular representation theory monster group normal subgroup number theory orthogonal group prentice hall presentation of a group primary cyclic group prime ideal prime number quantum group quotient group representation theory of finite groups ring homomorphism root of unity rotational symmetry semidirect product simple group special linear group special unitary group subgroup symmetric group symmetry group symplectic group unitary group up to