## Lectures on topics in the theory of infinite groups |

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### Contents

Incroduction definitions and relations | 1 |

Generators and relations | 12 |

Homomorphisms of groups | 25 |

9 other sections not shown

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### Common terms and phrases

abelian group algebraic systems amalgamated subgroup B.H. Neumann binary relation Burnside Conjecture Cartesian product central series Chapter commutes congruence in G Corollary defining relations definition denote direct product E-subgroup of H easy to verify element of G embedded embeds the amalgam endomorphism epimorphism equivalence relation factor groups family of groups following theorem free group G into H generalised direct product generalised free product gp(E group G group of order H is central Hence homomorphism homomorphism of G Hopf group inner automorphisms isomorphic kernel Kurosh lemma Let G locally finite group metabelian group monomorphism multiplication neutral element nilpotent group non-Hopf group normal subgroup normal word notation permutation group permutational product Proof prove quotient group relation in G s,t h Similarly soluble groups soluble of length splitting extension subgroup H subgroup of G subset unit element variety verbal subgroup word problem wreath product