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There is exactly one compact 1-dimensional Lie group having 27 components and nilpotence class three. We give a presentation for the integral cohomology ring of (the classifying space of) this group. We show that the groups of order 3 4 can be distinguished by their first few integral cohomology...
Let A be a finite-dimensional K -algebra over an algebraically closed field K and mod A be the category of finitely generated right A -modules. Following (1), A is said to be cycle-finite if, for every cycle M 0 → m 1 → … → M n = M 0 of non-zero non-isomorphisms between indecomposable...
In this note we shall construct a finite group G which has an automorphism α, which is not inner; however, the induced automorphism on SG is inner, where S is the ring of algebraic integers in a suitably chosen algebraic number field. A consequence of our arguments is that α is inner in KG for...
An isomorphism of group cohomology and equivariant cohomology yields a variation of a theorem of P. Webb, describing the p -component of the cohomology with trivial integer coefficients of certain finite groups as an alternating sum of cohomologies of local subgroups.
Following a remark of Lawvere, we explicitly exhibit a particularly elementary bijection between the set T of finite binary trees and the set T 7 of seven-tuples of such trees. “Particularly elementary” means that the application of the bijection to a seven-tuple of trees involves case...
In this paper, we begin the study of Bousfield classes for cohomology theories defined on spectra. Our main result is that a map f : X → Y induces an isomorphism on E ( n )-cohomology if and only if it induces an isomorphism on E ( n )-homology. We also prove this for variants of E(n) such as...
In this paper, we show that for every finite group with cyclic Sylow p -subgroups the principal p -block B is rigid with respect to the trivial simple module. This means that each autoequivalence which fixes the trivial simple module fixes the isomorphism class of each finitely generated B...
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