The finite unipotent groups consisting of bireflections

Let k be a field of characteristic p and V a finite dimensional k-vector space. An element g ? GL(V) is called a bireflection if it centralizes a subspace of codimension less than or equal to 2. It is known by a result of Kemper, that if for a finite p-group G ? GL(V) the ring of invariants Sym(V?) G is Cohen-Macaulay, G is generated by bireflections. Although the converse is false in general, it holds in special cases e.g. for particular families of groups consisting of bireflections. In this paper we give, for p > 2, a classification of all finite unipotent subgroups of GL(V) consisting of bireflections. Our description of the groups is given explicitly in terms useful for exploring the corresponding rings of invariants. This further analysis will be the topic of a forthcoming paper.