The Theory of Groups: An Introduction

a₁ abelian group additive assume automorphism basis called Chapter characteristic commutative complete composition conjugate consider construction contains COROLLARY correspondence coset defined Definition denote determined diagram direct sum distinct divides element equation equivalence exact example Exercise exists extension factor set field finite finite group fixed follows free abelian free group function functor G contains given gives group G group of order hence holds homomorphism ideal identity implies induction infinite integers isomorphism Lemma length Let G letters liftings machine matrix maximal multiplication nilpotent normal subgroup notation Observe one-to-one operation permutation polynomial positive presentation prime problem Proof Proof Let proper Prove pure rank rationals reader reduced relations ring root says sequence similar simple solvable subgroup of G subset summand Suppose theorem torsion-free unique vector space