Finite groups in which every two elements generate a soluble subgroup
Book information
Description
UK.: Birmingham. [Invent. Math. 121 (1995) No. 2, 279-285, eBook, English]We will prove the following result: Theorem. Let G be a finite group in which every two elements generate a soluble subgroup. Then G is soluble. This result was first obtained by John Thompson as a by-product of his classification of N -groups [7]. The proof we present is short and direct. It does not use any classification theorem. The possibility of obtaining results of this type by direct means was first realized by Martin Powell who proved that a finite group in which every three elements generate a soluble subgroup is soluble. An account of his work can be found in [2, pages 473-476]. Powell’s argument uses the Hall-Higman Theorem B. We use a different strategy that we shall now describe.Contents Introduction Preliminaries Normal p-subgroups Normal p'-subgroups Proof of Main Theorem References
Similar books
Рациональные подмножества в группах
Highly complex proofs and implications of such proofs
The Status of the Classification of the Finite Simple Groups
On the Fitting height of a soluble group that is generated by a conjugacy class
A Hall-Higman-Shult Type Theorem for Arbitrary Finite Groups
Теория полугрупп и ее приложения
DJVU
Разложение группы по подгруппе
Абстрактная теория групп
DJVU