On intervals in subgroup lattices of finite groups

• Autores: Michael Aschbacher
• Localización: Journal of the American Mathematical Society, ISSN 0894-0347, Vol. 21, Nº 3, 2008, págs. 809-830
• Idioma: inglés
• DOI: 10.1090/s0894-0347-08-00602-4
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• Resumen

  • We investigate the question of which finite lattices are isomorphic to the lattice of all overgroups of a subgroup in a finite group . We show that the structure of is highly restricted if is disconnected. We define the notion of a ``signalizer lattice" in and show for suitable disconnected lattices , if is minimal subject to being isomorphic to or its dual, then either is almost simple or admits a signalizer lattice isomorphic to or its dual. We use this theory to answer a question in functional analysis raised by Watatani