Groups containing a strongly embedded subgroup

• Autores: D. V. Lytkina, V. D. Mazurov
• Localización: Algebra and logic, ISSN 0002-5232, Vol. 48, Nº. 2, 2009, págs. 108-114
• Idioma: inglés
• DOI: 10.1007/s10469-009-9046-0
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• Resumen

  • An involution v of a group G is said to be finite (in G) if vv g has finite order for any g ? G. A subgroup B of G is called a strongly embedded (in G) subgroup if B and G\B contain involutions, but B ? B g does not, for any g ? G\B. We prove the following results. Let a group G contain a finite involution and an involution whose centralizer in G is periodic. If every finite subgroup of G of even order is contained in a simple subgroup isomorphic, for some m, to L 2(2 m ) or Sz(2 m ), then G is isomorphic to L 2(Q) or Sz(Q) for some locally finite field Q of characteristic two. In particular, G is locally finite (Thm. 1). Let a group G contain a finite involution and a strongly embedded subgroup. If the centralizer of some involution in G is a 2-group, and every finite subgroup of even order in G is contained in a finite non-Abelian simple subgroup of G, then G is isomorphic to L 2(Q) or Sz(Q) for some locally finite field Q of characteristic two (Thm. 2).