quasisimple group
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Quasisimple group — In mathematics, a quasisimple group (also known as a covering group) is a group that is a perfect central extension E of a simple group S . In other words, there is a short exact sequence:1 rarr; Z ( E ) rarr; E rarr; S rarr; 1such that E = [ E … Wikipedia
Component (group theory) — In mathematics, in the field of group theory, a component of a finite group is a quasisimple subnormal subgroup. Any two distinct components commute. The product of all the components is the layer of the group. For finite abelian (or nilpotent)… … Wikipedia
List of group theory topics — Contents 1 Structures and operations 2 Basic properties of groups 2.1 Group homomorphisms 3 Basic types of groups … Wikipedia
Binary icosahedral group — In mathematics, the binary icosahedral group is an extension of the icosahedral group I of order 60 by a cyclic group of order 2. It can be defined as the preimage of the icosahedral group under the 2:1 covering homomorphism:mathrm{Sp}(1) o… … Wikipedia
Profinite group — In mathematics, profinite groups are topological groups that are in a certain sense assembled from finite groups; they share many properties with their finite quotients. Definition Formally, a profinite group is a Hausdorff, compact, and totally… … Wikipedia
Projective linear group — In mathematics, especially in area of algebra called group theory, the projective linear group (also known as the projective general linear group) is one of the fundamental groups of study, part of the so called classical groups. The projective… … Wikipedia
Classification of finite simple groups — Group theory Group theory … Wikipedia
Schur multiplier — In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group of a group G. It was introduced by Issai Schur (1904) in his work on projective representations. Contents 1 Examples and properties 2 Re … Wikipedia
List of mathematics articles (Q) — NOTOC Q Q analog Q analysis Q derivative Q difference polynomial Q exponential Q factor Q Pochhammer symbol Q Q plot Q statistic Q systems Q test Q theta function Q Vandermonde identity Q.E.D. QED project QR algorithm QR decomposition Quadratic… … Wikipedia
Cosocle — In mathematics, the term cosocle has several related meanings. In group theory, a cosocle of a group G, denoted by Cosoc(G), is the intersection of all maximal normal subgroups of G.[1] If G is a quasisimple group, then Cosoc(G) = Z(G).[1] In the … Wikipedia
Fitting subgroup — In mathematics, especially in the area of algebra known as group theory, the Fitting subgroup F of a finite group G , named after Hans Fitting, is the unique largest normal nilpotent subgroup of G . Intuitively, it represents the smallest… … Wikipedia
