W.J Wong

Abelian unipotent subgroups of finite orthogonal groups

If G is the special orthogonal group O + (V) of a quadratic space V over a finite field of characteristic p , and r is a positive integer, we determine the abelian p -subgroups of largest order in G whose fixed subspaces in V have dimension at least r . In particular, we determine the abelian subgroups of largest order in a Sylow p -subgroup of G , extending some results obtained with different methods by Barry (1979).

Rank 1 preservers on the unitary Lie ring

The surjective additive maps on the Lie ring of skew-Hermitian linear transformations on a finite-dimensional vector space over a division ring which preserve the set of rank 1 elements are determined. As an application, maps preserving commuting pairs of transformations are determined.