The Theory of GroupsPerhaps the first truly famous book devoted primarily to finite groups was Burnside's book. From the time of its second edition in 1911 until the appearance of Hall's book, there were few books of similar stature. Hall's book is still considered to be a classic source for fundamental results on the representation theory for finite groups, the Burnside problem, extensions and cohomology of groups, p-groups and much more. For the student who has already had an introduction to group theory, there is much treasure to be found in Hall's Theory of Groups. |
Contents
I | 1 |
II | 26 |
III | 35 |
IV | 43 |
V | 53 |
VI | 84 |
VII | 91 |
VIII | 115 |
XI | 176 |
XII | 193 |
XIII | 200 |
XIV | 218 |
XV | 247 |
XVI | 311 |
XVII | 320 |
XVIII | 339 |
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Common terms and phrases
a₁ Abelian group absolutely irreducible algebraic automorphism B₁ basic commutators basis C₁ collineation commutators of weight composition series conjugate COROLLARY correspondence cyclic group define definition direct product division ring element of order elements of G exponent factor group finite group finite number fixed free group G contains G₁ given group G group of order H₁ h₂ Hence homomorphism idempotent identity induction integers intersection inverse isomorphic lattice left cosets LEMMA length Let G letters linear M₁ mapping matrix maximal subgroup modulo multiplication N₁ nilpotent normal subgroup p-group p-subgroup P₁ permutation group points Proof proper subgroup prove quaternion group R₁ relations representation of G S₁ satisfies solvable solvable group subgroup H subgroup of G subgroup of order supersolvable suppose Sylow subgroup Sylow theorem THEOREM translation plane u₁ unique whence y₁ zero