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- W4286970147 abstract "The investigation of the graph $mathcal{G}_p$ associated with the finite $p$-groups of maximal class was initiated by Blackburn (1958) and became a deep and interesting research topic since then. Leedham-Green and McKay (1976-1984) introduced skeletons of $mathcal{G}_p$, described their importance for the structural investigation of $mathcal{G}_p$ and exhibited their relation to algebraic number theory. Here we go one step further: we partition the skeletons into so-called Galois trees and study their general shape. In the special case $p geq 7$ and $p equiv 5 bmod 6$, we show that they have a significant impact on the periodic patterns of $mathcal{G}_p$ conjectured by Eick, Leedham-Green, Newman and O'Brien (2013). In particular, we use Galois trees to prove a conjecture by Dietrich (2010) on these periodic patterns." @default.
- W4286970147 created "2022-07-25" @default.
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- W4286970147 date "2021-09-20" @default.
- W4286970147 modified "2023-09-26" @default.
- W4286970147 title "Galois trees in the graph of $p$-groups of maximal class" @default.
- W4286970147 doi "https://doi.org/10.48550/arxiv.2109.09355" @default.
- W4286970147 hasPublicationYear "2021" @default.
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