Theorem describing fusion of elements in Sylow subgroup of finite group
In abstract algebra, the focal subgroup theorem describes the fusion of elements in a Sylow subgroup of a finite group. The focal subgroup theorem was introduced in (Higman 1953) and is the "first major application of the transfer" according to (Gorenstein, Lyons & Solomon 1996, p. 90). The focal subgroup theorem relates the ideas of transfer and fusion such as described by Otto Grün in (Grün 1936). Various applications of these ideas include local criteria for p-nilpotence and various non-simplicity criteria focussing on showing that a finite group has a normal subgroup of index p.
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detailed information about the number of subgroups of fixed order that a given finite group contains. The Sylow theorems form a fundamental part of finite group...
at Focal subgroup theorem: Subgroups and elaborated at focalsubgrouptheorem. There are three important normal subgroups of prime power index, each being...
kernels of the reflection maps are important objects of study; see focalsubgrouptheorem. The category of groups is a coreflective subcategory of the category...
duality. The dual group V^ to V is again a real vector space, and its closed subgroup L^ dual to L turns out to be a lattice in V^. Therefore, L^ is the natural...
theorem, stemming from this work, shows that if a scene consisting of five points is viewed from two cameras with unknown positions but known focal lengths...
early algebraic symbolism in the Maghreb, the Thabit number and Thābit theorem by Thābit ibn Qurra, the discovery of several new trigonometric identities...
electrical field) and Lagrangian orbits. Group theory: Lagrange's theorem of groups (a subgroup's order must always divide the order of the group exactly) represents...
2. A focal curve, surface and so on is the locus of the focal points of a family of linear subspaces. (Semple & Roth 1949, p.252) focus A focal point...
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