Group Theory, Volume 2 |
Common terms and phrases
A-invariant abelian group abelian normal subgroup abelian subgroup Assume assumption automorphism B₁ central product CG(t CG(x Chapter characteristic subgroup Clearly commutator subgroup conjugacy classes conjugate contradicts coset cyclic group defined definition derived group direct product element g element of order elementary abelian extraspecial factor group finite group following propositions Frobenius functor fusion G contains g of G G satisfies G₁ group G group of order H₁ Hence holds homomorphism implies inductive hypothesis integer involution irreducible characters irreducible representation isomorphic lemma Let G Let H matrix maximal subgroup minimal normal subgroup NG(P nilpotent group nonabelian nontrivial odd order p-group p-nilpotent p-solvable P₁ prime number proof of Theorem proper subgroup Prove the following Q₁ quaternion group S-subgroup satisfies condition shows simple group solvable group subgroup H subgroup of G subgroup of order subset subspace Suppose Sylow U₁ V₁ X₁