A course in the theory of groups
"An excellent up-to-date introduction to the theory of groups. It is general yet comprehensive, covering various branches of group theory. The 15 chapters contain the following main topics: free groups and presentations, free products, decompositions, Abelian groups, finite permutation groups, representations of groups, finite and infinite soluble groups, group extensions, generalizations of nilpotent and soluble groups, finiteness properties." --ACTA SCIENTIARUM MATHEMATICARUM
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2-transitive abelian group abelian subgroup Aut G automorphism Carter subgroups centre commutative conjugate contains coset countable cyclic groups deduce define denote direct product element of G elementary abelian equivalent Exercise extension F-representation finite group finite index finite soluble group follows Frat G free abelian free group free product Frobenius group g e G G is soluble G-module group and let group G group of order homomorphism implies induction infinite cyclic irreducible isomorphic Lemma Let G Let H locally finite group locally nilpotent group mapping matrix maximal subgroup minimal condition minimal normal subgroup module morphism nontrivial p-group p-nilpotent permutation group polycyclic group prime Proof Prove that G quotient group simple group soluble group subgroup H subgroup of G subnormal subgroups subset supersoluble Suppose that G Sylow p-subgroup system normalizer theorem torsion group torsion-free transitive transversal trivial unique write