theories.group_theory

Group theory (especially finite group theory).

subgroup : general subgroup theories, quotient group using quot
finsubg : finite subgroups (finset and fintype), Lagrange theorem, finite cosets and lcoset_type, normalizer for finite groups, coset product and quotient group based on lcoset_type, semidirect product
hom : homomorphism and isomorphism, kernel, first isomorphism theorem
perm : permutation group
cyclic : cyclic subgroup, finite generator, order of generator, sequence and rotation
action : fixed point, action, stabilizer, orbit stabilizer theorem, orbit partition, Cayley theorem, action on lcoset, cardinality of permutation group
pgroup : subgroup with order of prime power, Cauchy theorem, first Sylow theorem