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
โฆ LIBER โฆ
Locally graduated groups, factorizable by subgroups of finite rank
โ Scribed by N. S. Chernikov
- Publisher
- Springer US
- Year
- 1982
- Tongue
- English
- Weight
- 718 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0002-5232
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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
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