Nilpotent extensions of blocks

Extensions of Nilpotent P.P. Rings

extensions of nilpotent p.p. rings

A Characterisation of Nilpotent Blocks

Let B be a p-block of a finite group, and set m = ∑ χ(1), the sum taken over all height zero characters of B. Motivated by a result of M. Isaacs characterising p-nilpotent finite groups in terms of character degrees, we show that B is nilpotent if and only if the exact power of p dividing m is equal to the p-part of |G : P ||P : R|, where P is a defect group of B and where R is the focal subgro...

A note on extensions of nilpotent groups

A further advance—though it was not presented as such—was contained in Theorem 1.6 of [1], which effectively gave an example showing that the answer to our question is not always affirmative. The main purpose of this paper is to generalize both Theorem 0.1 and the counterexample contained in Theorem 1.6 of [1]. Thus we prove (cf. Theorems 2.1 and 2.3, which reproduce part (b) and part (a) of Th...

Essential Extensions and the Nilpotent Filtration

The spectral sequence associated to the Arone-Goodwillie tower for the n-fold loop space functor is used to show that the first two non-trivial layers of the nilpotent filtration of the reduced mod 2 cohomology of a (sufficiently connected) space with nilpotent cohomology are comparable. This relies upon the theory of unstable modules over the mod 2 Steenrod algebra, together with properties of...