Supervarieties of small graded colength

Let A be a superalgebra over a field F of characteristic zero, and let , n=1,2,…, be the sequence of graded cocharacters of A. For every n≥1, let denote the nth graded colength of A, counting the number of Z2≀Sn-irreducibles appearing in . In this article, we classify the finite dimensional superalgebras A such that the sequence of graded colengths, , is bounded by two. Moreover, we prove that there is a finite number of superalgebras A1,…,Aq such that if and only if A1,…,Aq∉vargr(A).