Geodesic
On intervals in subgroup lattices of finite groups
Aschbacher, Michael1
1Department 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 
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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