FINITE p-GROUPS AND COCLASS THEORY

On the construction of CF pro-p-groups by coclass

The classification of finite p-groups is an often examined area of group theory. In this talk the classification by coclass is investigated for the special class of CF groups. These groups were introduced by Norman Blackburn as a generalisation of groups of maximal class. The coclass-project will be established for background knowledge. It was initialised by Charles Leedham-Green and Mike Newma...

FINITE p-GROUPS IN REPRESENTATION THEORY

Classifying 2-groups by Coclass

Now that the conjectures of Leedham-Green and Newman have been proved, we probe deeper into the classification of p-groups using coclass. We determine the pro-2-groups of coclass at most 3 and use these to classify the 2-groups of coclass at most 3 into families. Using extensive computational evidence, we make some detailed conjectures about the structure of these families. We also conjecture t...

Pairwise‎ ‎non-commuting elements in finite metacyclic $2$-groups and some finite $p$-groups

Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.

Finite Groups with p-Sylow Coverings