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Author Broto, C. ♦ Castellana, N. ♦ Grodal, J. ♦ Levi, R. ♦ Oliver, B.
Source CiteSeerX
Content type Text
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Classifying Space ♦ Subgroup Family ♦ P-constrained Finite Group ♦ Off-centricf-radical Subgroup ♦ Constrained Fusion System ♦ Sylow P-subgroup ♦ F-quasicentric Subgroup ♦ P-local Finite Group ♦ Homotopy Type ♦ Finite Group ♦ Abstract Fusion Systemf ♦ Conjugacy Relation ♦ Enough Information ♦ Finite P-group
Description A p-local finite group consists of a finite p-group S, together with a pair of categories which encode “conjugacy ” relations among subgroups of S, and which are modelled on the fusion in a Sylow p-subgroup of a finite group. It contains enough information to define a classifying space which has many of the same properties as p-completed classifying spaces of finite groups. In this paper, we examine which subgroups control this structure. More precisely, we prove that the question of whether an abstract fusion systemF over a finite p-group S is saturated can be determined by just looking at smaller classes of subgroups of S. We also prove that the homotopy type of the classifying space of a given p-local finite group is independent of the family of subgroups used to define it, in the sense that it remains unchanged when that family ranges from the set ofF-centricF-radical subgroups (at a minimum) to the set of F-quasicentric subgroups (at a maximum). Finally, we look at constrained fusion systems, analogous to p-constrained finite groups, and prove that they in fact all arise from groups. A p-local finite group consists of a finite p-group S, together with a pair of categories (F, L), of which F is modeled on the conjugacy (or fusion) in a Sylow
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 2005-01-01
Publisher Institution Proc. London Math. Soc. 91