## An introduction to the theory of groupsAnyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book. The first six chapters provide material for a first course, while the rest of the book covers more advanced topics. This revised edition retains the clarity of presentation that was the hallmark of the previous editions. From the reviews: "Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route." --MATHEMATICAL REVIEWS |

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### Contents

ll | 5 |

THE ISOMORPHISM THEOREMS ll | 11 |

PERMUTATION GROUPS | 32 |

Copyright | |

14 other sections not shown

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### Common terms and phrases

Assume Aut(K automorphism commute composition series conjugacy classes conjugate Corollary cosets cyclic groups deﬁned Deﬁnition Deﬁnition Let denoted direct product direct sum disjoint divisor element of order elements of G example Exercise exists factor groups factor set ﬁnite abelian group ﬁnite group ﬁnitely presented ﬁrst ﬁxed ﬁxes follows free abelian function G acts G contains G-set group G group of order hence HINT HNN extension homomorphism ideal implies induction inﬁnite integer k-transitive kernel Lemma Let F Let G Let H matrix multiplicative group nilpotent nonabelian nonabelian group nonsingular nonzero normal series normal subgroup notation one-one correspondence p-group p-primary permutation polynomial prime Proof Let Prove that G reader semidirect product semigroup semilinear shows simple group solvable group Steiner system subgroup H subgroup of G subgroup of order subset subspace sufﬁces summands Sylow p-subgroup transitive G-set transpositions transvection unique vector space