Classifying Spaces Of Sporadic Groups
Download Classifying Spaces Of Sporadic Groups PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Classifying Spaces Of Sporadic Groups book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Classifying Spaces of Sporadic Groups
Author: David J. Benson
language: en
Publisher: American Mathematical Soc.
Release Date: 2008
For each of the 26 sporadic finite simple groups, the authors construct a 2-completed classifying space using a homotopy decomposition in terms of classifying spaces of suitable 2-local subgroups. This construction leads to an additive decomposition of the mod 2 group cohomology.
Equivalences of Classifying Spaces Completed at the Prime Two
Author: Robert Oliver
language: en
Publisher: American Mathematical Soc.
Release Date: 2006
We prove here the Martino-Priddy conjecture at the prime $2$: the $2$-completions of the classifying spaces of two finite groups $G$ and $G'$ are homotopy equivalent if and only if there is an isomorphism between their Sylow $2$-subgroups which preserves fusion. This is a consequence of a technical algebraic result, which says that for a finite group $G$, the second higher derived functor of the inverse limit vanishes for a certain functor $\mathcal{Z}_G$ on the $2$-subgroup orbit category of $G$. The proof of this result uses the classification theorem for finite simple groups.
Applying the Classification of Finite Simple Groups
Author: Stephen D. Smith
language: en
Publisher: American Mathematical Soc.
Release Date: 2018-04-30
Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a second-year graduate course for students who have had first-year graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.