On the Irreducible Carpets of Additive Subgroups of Type.

We consider the irreducible carpets of type over an algebraical extension of a field such that all additive subgroups are -modules. The carpets, parametrized by a pair of additive subgroups, appear only in characteristic 2. This pair of additive subgroups presents (possibly different) fields up to conjugation by a diagonal element in the corresponding Chevalley group. Moreover, we establish that such carpets are closed. Using Levchuk's description of the irreducible carpets of Lie type of rank greater than 1 over , we show that all additive subgroups of the carpets coincide with an intermediate subfield between and of the carpets of types , , and in case of the characteristic of is not 0 and 2 whereas it is neither 0, 2, nor 3 for type up to conjugation by a diagonal element. [ABSTRACT FROM AUTHOR]