Subgroups of Classical Groups Generated by Long Root Elements

DOI10.2307/1998972zbMath0406.20040OpenAlexW4246738913MaRDI QIDQ4192254

William M. Kantor

Publication date: 1979

Full work available at URL: https://doi.org/10.2307/1998972

zbMATH Keywords

Conjugacy ClassesConjugacy Class of Long Root ElementsLong Root GroupSubgroups of Classical Groups of Characteristic P

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Generators, relations, and presentations of groups (20F05)

Related Items (67)

Maximal subgroups of symplectic groups stabilizing spreads ⋮ Primitive permutation groups of odd degree, and an application to finite projective planes ⋮ Geometry of root elements in groups of type $\mathrm E_{6}$ ⋮ Classification of subgroups of symplectic groups over finite fields containing a transvection. ⋮ The transvection free groups with polynomial rings of invariants ⋮ On twisted tensor product group embeddings and the spin representation of symplectic groups ⋮ A quick geometrical proof that \(G_ 2(K)\) is maximal in \(P\Omega _ 7(K)\) ⋮ Real constituents of permutation characters ⋮ Hall-Higman type theorems for exceptional groups of Lie type. I ⋮ The 2F-modules for nearly simple groups. ⋮ Reduction theorems for triples of short root subgroups in Chevalley groups ⋮ Infinite alternating groups as finitary linear transformation groups ⋮ Generating sets of root elements of Chevalley groups over a field ⋮ Groups with a \(p\)-element acting with a single non-trivial Jordan block on a simple module in characteristic \(p\) ⋮ Fixed point ratios in actions of finite classical groups. II. ⋮ The finite irreducible linear groups with polynomial ring of invariants ⋮ Permutation representations of the finite classical groups of small degree or rank ⋮ Presentations of finite simple groups: a computational approach. ⋮ Maximal subgroups of \(GL_{2n}(K), SL_{2n}(K), PGL_{2n}(K)\) and \(PSL_{2n}(K)\) associated with symplectic polarities ⋮ Fischer subspaces of Hermitian manifolds ⋮ Fusion systems with J-components over \(F_{2^e}\) with \(e>1\) ⋮ Maximal subgroups of \(G_2(2^n)\) ⋮ Maximal subgroups of the orthogonal group ⋮ Subgroups of exceptional groups of Lie type generated by long root elements. I. Odd characteristic ⋮ Subgroups of exceptional groups of Lie type generated by long root elements. II. Characteristic two ⋮ Overgroups of root groups in classical groups ⋮ The Gorenstein property for modular binary forms invariants ⋮ Subgroups of split orthogonal groups over a ring ⋮ Some subgroups of SL(n,\(2^ m)\). I ⋮ Generation of finite almost simple groups by conjugates. ⋮ Unnamed Item ⋮ A characterization of finite symplectic groups over fields with more than two elements ⋮ Fixed point ratios in actions of finite classical groups. IV. ⋮ Subgroups of a spinor group containing a maximal split torus. I ⋮ 3-transposition groups with non-central normal 2-subgroups ⋮ Constructive recognition of \(\text{SL}_3(q)\). ⋮ Subgroups of simple algebraic groups containing regular tori, and irreducible representations with multiplicity 1 non-zero weights ⋮ Probabilistic generation of finite simple groups. II. ⋮ Linear groups ⋮ An algorithm of Katz and its application to the inverse Galois problem. ⋮ Finite groups ⋮ On the generation of some embeddable GF(2) geometries ⋮ Subgroups of Lie type groups containing the center of a unipotent radical. ⋮ Subgroups of Lie type groups containing a unipotent radical. ⋮ On twisted tensor product group embeddings and the spin representation of symplectic groups: the case \(q\) odd. ⋮ Reflection Groups ⋮ Geometry of 1-tori in $\mathrm {GL}_n$ ⋮ Image of the Artin groups of classical types inside the finite Iwahori-Hecke algebras ⋮ Quasiprimitve linear groups with quadratic elements ⋮ Image of the braid groups inside the finite Temperley-Lieb algebras. ⋮ Minimal degree for a permutation representation of a classical group ⋮ Subsystem subgroups of the group of type $\mathrm {F}_4$ generated by short root subgroups ⋮ On the geometry of the exceptional group \(G_2(q)\), \(q\) even ⋮ Generation of pairs of short root subgroups in Chevalley groups ⋮ On the geometry of the adjoint representation of a Chevalley group ⋮ Solvability of finite coatomic groups ⋮ Finite quotients of the pure symplectic braid group ⋮ On the generation of dual polar spaces of symplectic type over finite fields ⋮ Subgroups isomorphic to \(G_2(L)\) in orthogonal groups ⋮ Abstract root subgroups and quadratic action. With an Appendix by A. E. Zalesskii ⋮ Arithmetic of division fields ⋮ Some aspects of finite linear groups: A survey ⋮ Black box exceptional groups of Lie type ⋮ Probabilistic generation of finite simple groups ⋮ A criterion for the existence of normal \(\pi\) -complements in finite groups ⋮ Subgroups inducing the same permutation representation. II ⋮ Unnamed Item

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