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Author: Michael Aschbacher
Publisher: American Mathematical Soc.
Published: 1986
Total Pages: 242
ISBN-13: 0821823442
DOWNLOAD EBOOKThe maximal overgroups of noncyclic Sylow subgroups of the sporadic finite simple groups are determined. Moreover a geometric structure is associated to this collection of overgroups, which is useful in the study of sporadic groups.
Author: Michael Aschbacher
Publisher: American Mathematical Soc.
Published: 2016-04-26
Total Pages: 196
ISBN-13: 1470418452
DOWNLOAD EBOOKThe author extends results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular he determines the maximal subgroups of this form. He also determines the maximal overgroups of short root subgroups in finite classical groups and the maximal overgroups in finite orthogonal groups of c-root subgroups.
Author: C. M. Campbell
Publisher: Cambridge University Press
Published: 2007-01-04
Total Pages: 443
ISBN-13: 0521694701
DOWNLOAD EBOOKSelected papers from 'Groups St Andrews 2005' cover a wide spectrum of modern group theory.
Author: William M. Kantor
Publisher: Cambridge University Press
Published: 1995-01-12
Total Pages: 324
ISBN-13: 052146790X
DOWNLOAD EBOOKSilk Hope, NC is a buoyant and moving parable in which two good women find, among the hidden, forgotten virtues of the past, a sustenance to carry them into the future.
Author: Carles Broto
Publisher: American Mathematical Soc.
Published: 2020-02-13
Total Pages: 176
ISBN-13: 1470437724
DOWNLOAD EBOOKFor a finite group G of Lie type and a prime p, the authors compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic, with a very short list of exceptions. When p is different from the defining characteristic, the situation is much more complex but can always be reduced to a case where the natural map from Out(G) to outer automorphisms of the fusion or linking system is split surjective. This work is motivated in part by questions involving extending the local structure of a group by a group of automorphisms, and in part by wanting to describe self homotopy equivalences of BG∧p in terms of Out(G).
Author: David J. Benson
Publisher: American Mathematical Soc.
Published: 2008
Total Pages: 310
ISBN-13: 0821844741
DOWNLOAD EBOOKFor 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.
Author: Martin W. Liebeck
Publisher: Cambridge University Press
Published: 1992-09-10
Total Pages: 505
ISBN-13: 0521406854
DOWNLOAD EBOOKThis volume contains a collection of papers on the subject of the classification of finite simple groups.
Author: Stephen D. Smith
Publisher: American Mathematical Soc.
Published: 2011-11-10
Total Pages: 378
ISBN-13: 0821805010
DOWNLOAD EBOOKThis book is intended as an overview of a research area that combines geometries for groups (such as Tits buildings and generalizations), topological aspects of simplicial complexes from $p$-subgroups of a group (in the spirit of Brown, Quillen, and Webb), and combinatorics of partially ordered sets. The material is intended to serve as an advanced graduate-level text and partly as a general reference on the research area. The treatment offers optional tracks for the reader interested in buildings, geometries for sporadic simple groups, and $G$-equivariant equivalences and homology for subgroup complexes.
Author: Robert Oliver
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 116
ISBN-13: 0821838288
DOWNLOAD EBOOKWe 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.
Author: B. Hartley
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 469
ISBN-13: 9401103291
DOWNLOAD EBOOKThis volume contains the proceedings of the NATO Advanced Study Institute on Finite and Locally Finite Groups held in Istanbul, Turkey, 14-27 August 1994, at which there were about 90 participants from some 16 different countries. The ASI received generous financial support from the Scientific Affairs Division of NATO. INTRODUCTION A locally finite group is a group in which every finite set of elements is contained in a finite subgroup. The study of locally finite groups began with Schur's result that a periodic linear group is, in fact, locally finite. The simple locally finite groups are of particular interest. In view of the classification of the finite simple groups and advances in representation theory, it is natural to pursue classification theorems for simple locally finite groups. This was one of the central themes of the Istanbul conference and significant progress is reported herein. The theory of simple locally finite groups intersects many areas of group theory and representation theory, so this served as a focus for several articles in the volume. Every simple locally finite group has what is known as a Kegel cover. This is a collection of pairs {(G , Ni) liE I}, where I is an index set, each group Gi is finite, i Ni
