Full Description
Coclass is a powerful invariant that reveals patterns in the intricate landscape of finite p-groups. This monograph offers a gentle introduction to coclass theory, presenting key developments from the past two decades within a unified framework and discussing open conjectures. Alongside a systematic exposition of established results, the book presents new findings and some corrections to the literature. Special emphasis is placed on coclass graphs and their remarkable periodic structures. Intended for readers with a graduate-level background in group theory and algebra, the book is accessible to newcomers, including graduate students, while also serving as a reliable reference for researchers.
Contents
1 Introduction to coclass graphs.- 2 Constructive methods and visualisations.- 3 Number theory and group constructions.- 4 Matrix groups and uniseriality.- 5 Cohomology theory and extensions.- 6 The number of infinite paths in G¹ (p,r).- 7 Periodicity I.- 8 The skeletons of a coclass tree.- 9 Groups of maximal class.- 10 Towards Periodicity II.- References.- Index.- List of Symbols.
