CaltechAUTHORS
  A Caltech Library Service

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. https://resolver.caltech.edu/CaltechAUTHORS:ASCjams08

[img]
Preview
PDF - Published Version
See Usage Policy.

301kB

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:ASCjams08

Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1090/S0894-0347-08-00602-4DOIUNSPECIFIED
http://www.ams.org/jams/2008-21-03/S0894-0347-08-00602-4/home.htmlPublisherUNSPECIFIED
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
Funders:
Funding AgencyGrant Number
NSF0504852
Subject Keywords:INTERMEDIATE SUBFACTORS.
Issue or Number:3
DOI:10.1090/S0894-0347-08-00602-4
Record Number:CaltechAUTHORS:ASCjams08
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:ASCjams08
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13447
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:13 May 2009 21:07
Last Modified:08 Nov 2021 22:37

Repository Staff Only: item control page