On intervals in subgroup lattices of finite groups

Author:
Michael Aschbacher

Journal:
J. Amer. Math. Soc. **21** (2008), 809-830

MSC (2000):
Primary 20D30; Secondary 06B05, 46L37

Published electronically:
March 17, 2008

MathSciNet review:
2393428

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Abstract | References | Similar Articles | Additional Information

Abstract: 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.

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Additional Information

**Michael Aschbacher**

Affiliation:
Department of Mathematics, California Institute of Technology, Pasadena, California 91125

DOI:
https://doi.org/10.1090/S0894-0347-08-00602-4

Received by editor(s):
June 28, 2006

Published electronically:
March 17, 2008

Additional Notes:
This work was partially supported by NSF-0504852

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.