On structural aspects of finite simple groups of Lie type
Abstract
In this PhD thesis, we consider two problems that are related to finite simple groups
of Lie type. First of them is a problem mentioned in the Kourovka notebook: describe
the finite simple groups in which every element is a product of two involutions. We
consider the simple orthogonal groups in even characteristic, and solve the problem for
them. Since other groups have been dealt with elsewhere, the problem is then solved
completely.
The second part of the thesis is related to Lie algebras. Every complex simple
Lie algebra has a compact real form that is associated with a compact Lie group. In
this thesis, we consider the Lie algebra of type E8, and give a new construction of its
compact real form. The Lie product is defined using the irreducible subgroup of shape
25+10 ·GL5(2) of the automorphism group.
Authors
Ramo, Johanna MariaCollections
- Theses [3706]