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On intervals in subgroup lattices of finite groups

Aschbacher, Michael (2008) On intervals in subgroup lattices of finite groups. Journal of the American Mathematical Society, 21 (3). pp. 809-830. ISSN 0894-0347. doi:10.1090/S0894-0347-08-00602-4.

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

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Additional Information:© 2008 American Mathematical Society. Received by the editors June 28, 2006. Article electronically published on March 17, 2008. This work was partially supported by NSF-0504852. 20D30, 06B05, 46L37
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Issue or Number:3
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13447
Deposited By: Ruth Sustaita
Deposited On:13 May 2009 21:07
Last Modified:08 Nov 2021 22:37

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