Galois trees in the graph of p-groups of maximal class

The investigation of the graph Gp associated with finite p-groups maximal class was initiated by Blackburn (1958) and became a deep interesting research topic since then. Leedham-Green & McKay (1976–1984) introduced skeletons Gp, described their importance for structural exhibited relation to algebraic number theory. Here we go one step further: partition into so-called Galois trees study general shape. In special case p⩾7 p≡5mod6, show that they have significant impact on periodic patterns conjectured Eick, Leedham-Green, Newman O'Brien (2013). particular, use prove conjecture Dietrich (2010) these patterns.