Here is a unique guide devoted exclusively to a new and innovative area of mathematical study. The volume, prepared by internationally known experts in computational group theory, provides a systematic source of examples of finite perfect groups. Approaching the subject from both a theoretical and practical standpoint, this book includes discussion of the classification of finite perfect groups of small order and the use of infinite perfect groups to construct infinite sequences of finite perfect groups. These discussions will also provide informative material on subgraphs and asymptotic behavior. The second part of this valuable reference, which can be utilized independently or as part of a unified whole, gives the reader two sets of tables which provide fast access to most perfect groups of order up to one million, as well as low-dimensional perfect (crystallographic) space groups.
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Perfect groups with nontrivial Fitting subgroup
Systematic enumeration of finite perfect groups
Basic structure and enumeration of perfect space groups
5 other sections not shown
3-local multiplier abelian group absolutely irreducible Action of automorphisms associated lattices Bases of sublattices Centralizing algebra Cohomology on Lf compute corresponding cohomology class cover of 4,1 defined denoted Edges elements epimorphism Extension E2 extension of 24 factor groups faithful permutation representation finite group finite perfect groups form on Lf Frattini extension G-module Gram matrix graph of groups group G groups of order groups with point indecomposable module Inflation mod invariant quadratic form Irr(G Irreducible modules isomorphic to sublattices isomorphism classes isomorphism types Lattices of rank Lemma Let G matrix for invariant module relations Nonsplit extension Orbit representatives Order of corresponding outer automorphism p-groups Perfect extensions perfect groups Perfect space groups point group Presentation of point product of l,1 profinite groups PROOF Proposition quasisimple groups scalars Split extension Stabilizer Subdirect product subgroup for V2 systems and associated Translation subgroup Vector systems Vj trivial