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Locally (Soluble-by-Finite) Groups of Finite Rank

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

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 178 KB
Volume: 182
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0200

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✦ Synopsis

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 therefore has order at most s and it follows that P F E . Again by 2 Lemma 2.2, PN rN is soluble and hence trivial. Thus P F N s K = L 2 2 2 2 2

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