The collected works of Philip Hall
As one of the world's most influential algebraists, Philip Hall is renowned for groundbreaking work in his field. The papers in this collection of his works are models of lucidity that offer relevant information for today's mathematicians and group theorists. The sequence of papers on soluble groups, up to and including his Hall-Higman paper and one on "Theorems Like Sylow's", are of fundamental importance to the development of finite group theory. Also included is Hall's Queen Mary College Mathematics Notes volume, which remains an excellent introduction to nilpotent groups.
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Trans Amer Math Soc 39 1936 49699
Quart J Math 7 1936 134151
A partition formula connected with Abelian groups
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Abelian group Abelian subgroup algebra belongs Burnside characteristic subgroup chief factors commutator subgroup congruent conjugate corollary corresponding coset defined definition denote derived group direct product elements of G equal equation factor groups factor of G finite group finite order follows formula free group G satisfies given group G group of automorphisms group of order Hall Hence homomorphism hypothesis induction inner automorphisms integer invariant isoclinic isomorphic Lemma Let G London Math lower central series maximal Mobius function nilpotent group normal in G normal subgroup number of solutions obtain order of G order pn p-group p-subgroup partition permutable polycyclic groups prime prime-power groups proof proper subgroup prove pure situations quotient group result satisfies Max-n self-conjugate subgroup series of G soluble groups stem groups subgroup of G subgroups of order suppose Sylow complements Sylow subgroups Sylow system system normalizer Theorem theory