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Locally (soluble-by-finite) groups with all proper insoluble subgroups of finite rank

โœ Scribed by Martyn R. Dixon; Martin J. Evans; Howard Smith

Publisher
Springer
Year
1997
Tongue
English
Weight
611 KB
Volume
68
Category
Article
ISSN
0003-889X

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๐Ÿ“œ SIMILAR VOLUMES

Locally Finite Groups with All Subgroups
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โœ E.I Khukhro; H Smith ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 194 KB

A group is said to have finite special rank F s if all of its finitely generated subgroups can be generated by s elements. Let G be a locally finite group and suppose that HrH has finite rank for all subgroups H of G, where H denotes the normal core of H in G. We prove that then G has an abelian no

Locally (Soluble-by-Finite) Groups of Fi
Locally (Soluble-by-Finite) Groups of Finite Rank
โœ Martyn R. Dixon; Martin J. Evans; Howard Smith ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 178 KB

But P l B s rad P and so L ( Prrad P. It remains to show that P F L . 1 2 If Q is a maximal normal subgroup of P then, since P is perfect, PrQ is isomorphic to a simple direct factor of L and hence has order greater 1 than s. With the notation as in Lemma 2.2, we have PE rE ( PrP l E , 2 2 2 which t