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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a₁ abelian group abelian subgroup automorphism Carter subgroups commutative conjugate contains coset cyclic groups define denote direct product element of G elementary abelian Exercise F-covering subgroup FG-module finite group finite index finite soluble group follows Frat G free group free product Frobenius group g in G G₁ G₂ group G group of order H₁ homomorphism implies induction infinite cyclic integer irreducible isomorphic k-transitive K₁ Let F Let G Let H locally nilpotent locally nilpotent group M₁ mapping matrix maximal subgroup minimal normal subgroup morphism N₁ nilpotent group nontrivial normal closure normal form p-group p-nilpotent P₁ permutation group polycyclic group prime Proof Prove that G quotient group simple group sn G soluble group subgroup H subgroup of G subnormal subgroups subset supersoluble Suppose that G Sylow p-subgroup system normalizer Theorem torsion-free transitive transversal trivial write