A solvability condition for finite groups with nilpotent maximal subgroups

John Randolph

doi:10.1017/s0004972700045937

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A solvability condition for finite groups with nilpotent maximal subgroups

John Randolph

Year: 1970 Journal: Bulletin of the Australian Mathematical Society Vol: 3 (2)Pages: 273-276 Publisher: Cambridge University Press

DOI: 10.1017/s0004972700045937

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Abstract

Let G be a finite group with a nilpotent maximal subgroup S and let P denote the 2-Sylow subgroup of S . It is shown that if P ∩ Q is a normal subgroup of P for any 2-Sylow subgroup Q of G , then G is solvable.

Keywords:

Mathematics Sylow theorems Fitting subgroup Index of a subgroup Maximal subgroup Characteristic subgroup Nilpotent Complement (music) Combinatorics Normal subgroup Locally finite group p-group Finite group Group (periodic table) Symmetric group

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Finite Group Theory Research

Physical Sciences → Mathematics → Discrete Mathematics and Combinatorics

A solvability condition for finite groups with nilpotent maximal subgroups

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