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Intervals in the subgroup lattices of the alternating and symmetric groups of prime degree

Perepelitsky, Philipp (2009) Intervals in the subgroup lattices of the alternating and symmetric groups of prime degree. Journal of Group Theory, 12 (1). pp. 119-137. ISSN 1433-5883. https://resolver.caltech.edu/CaltechAUTHORS:20090901-112037824

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Abstract

If G is a group and H is a subgroup of G we write O_G(H) for the lattice of over-groups of H in G. It is an open question whether or not every finite lattice is isomorphic to some finite group interval lattice O_G(H), where G is finite. We prove that no DΔ(m1, … , mt)-lattice and few M-lattices have the form O_G(H), where G is an alternating or symmetric group of prime degree.


Item Type:Article
Related URLs:
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http://dx.doi.org/10.1515/JGT.2008.065DOIArticle
Additional Information:© 2009 de Gruyter. Received: 10/12/2007; revised: 04/03/2008; published online: 05/01/2009. Communicated by R. M. Guralnick. The author would like to express his warm thanks to Professor Aschbacher for all his help with this paper.
Issue or Number:1
Record Number:CaltechAUTHORS:20090901-112037824
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20090901-112037824
Official Citation:Journal of Group Theory. Volume 12, Issue 1, Pages 119–137, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: 10.1515/JGT.2008.065, /January/2009.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15522
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:01 Oct 2009 19:55
Last Modified:03 Oct 2019 00:58

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