Abstract
Let k be a field of characteristic p and V a finite-dimensional k-vector space.
An element
{g\in{\rm 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\leq{\rm GL}(V)}
the ring of invariants
{{\rm 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
{{\rm 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.