Subalgebras of Steenrod algebra and the action of matrices on truncated polynomial algebras (Q582627)

The authors' abstract reads: ``Let \(A(t)\) be the subalgebra of the Steenrod algebra generated by \(Sq^ i\), \(i\leq 2^ t\). We determine which \(A\)-module indecomposable summands of \({\mathbb{F}}_ 2[x_ 1,...,x_ n]\) are free over \(A(t)\) by first showing this to be equivalent to the group theoretic question of determining which irreducible modular representations of \(M_ n({\mathbb{F}}_ 2)\) (or \(GL_ n({\mathbb{F}}_ 2))\) occur as composition factors in the truncated polynomial algebra \({\mathbb{F}}_ 2[x_ 1,...,x_ n]/(x_ 1^{2^ t},...,x_ n^{2^ t}).\) The second question is then answered''. The paper uses an interplay of Steenrod algebra techniques and constructions of finite group theory and is motivated by a well known result of \textit{J. F. Adams}, \textit{J. H. Gunawardena} and \textit{H. Miller} [Topology 24, 435-460 (1985; Zbl 0611.55010)] which states that \[ End_ A({\mathbb{F}}_ 2[x_ 1,...,x_ n])\cong {\mathbb{F}}_ 2[M_ n({\mathbb{F}}_ 2)]. \]