We prove an old standing conjecture by showing that the lattice of subgroups of every finite simple group is a complemented lattice. We achieve this result by using the classification of finite simple groups, and information on the maximal subgroups.
The finite simple groups have complemented subgroup lattices
COSTANTINI, MAURO;ZACHER, GIOVANNI
2004
Abstract
We prove an old standing conjecture by showing that the lattice of subgroups of every finite simple group is a complemented lattice. We achieve this result by using the classification of finite simple groups, and information on the maximal subgroups.
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