Geodesic
On intervals in subgroup lattices of finite groups
Aschbacher, Michael1
1 Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Journal of the American Mathematical Society, Tome 21 (2008) no. 3, pp. 809-830

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-08-00602-4

Aschbacher, Michael 1

1 Department of Mathematics, California Institute of Technology, Pasadena, California 91125 
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Aschbacher, Michael. On intervals in subgroup lattices of finite groups. Journal of the American Mathematical Society, Tome 21 (2008) no. 3, pp. 809-830. doi: 10.1090/S0894-0347-08-00602-4

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