On a minimal set of generators for the algebra H ∗ ( B E d ; F 2 ) and its applications

We investigate the Peterson hit problem for polynomial algebra \(\mathcal P_{d}\), viewed as a graded left module over mod-\(2\) Steenrod algebra, \(\mathcal{A}\). For \(d>4\), this is still unsolved, even in case of \(d=5\) with help computers. In article, we study \(d=6\) generic degree \(6(2^{r}-1)+6.2^r\), \(r\) an arbitrary non-negative integer. Furthermore, behavior sixth Singer algebraic transfer \(6(2^{r}-1)+6.2^r\) also discussed at end paper.