Information om | Engelska ordet GROUP-THEORETIC

Exempel på hur man kan använda GROUP-THEORETIC i en mening

• Representations of groups allow many group-theoretic problems to be reduced to problems in linear algebra.
• Simple Lie groups include many classical Lie groups, which provide a group-theoretic underpinning for spherical geometry, projective geometry and related geometries in the sense of Felix Klein's Erlangen program.
• Easier, but still essential, results that use character theory include Burnside's theorem (a purely group-theoretic proof of Burnside's theorem has since been found, but that proof came over half a century after Burnside's original proof), and a theorem of Richard Brauer and Michio Suzuki stating that a finite simple group cannot have a generalized quaternion group as its Sylow -subgroup.
• Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators.
• Considering subgroups, and in particular maximal subgroups, of semigroups often allows one to apply group-theoretic techniques in semigroup theory.
• The group-theoretic notion of HNN (Higman-Neumann-Neumann) extension bears the names of Bernard and his wife Hanna, from their joint paper with Graham Higman (who later supervised the PhD of their son Peter).
• Among other works, he has shown the h-infinity-optimality of the least mean squares filter, used group-theoretic techniques to design space-time codes and frames and to study entropic vectors, performed information-theoretic studies of various wireless networks (such as determining the capacity of the MIMO wiretap channel), constructed tree codes for interactive communication and control, developed various algorithms and performance analyses for compressed sensing and structured signal recovery, studied epidemic spread in complex networks, and co-invented real-time DNA microarrays.
• Henry Cohn, Robert Kleinberg, Balázs Szegedy and Chris Umans put methods such as the Strassen and Coppersmith–Winograd algorithms in an entirely different group-theoretic context, by utilising triples of subsets of finite groups which satisfy a disjointness property called the triple product property (TPP).
• Bipartite Cayley graphs give a way from translating quasirandomness in the graph-theoretic setting to the group-theoretic setting.

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