Two-Dimension Projective Linear Groups Act Block-Transitively on 5-(q + 1, 6, λ) Designs

2019 ◽  
Vol 09 (06) ◽  
pp. 694-698
Author(s):  
乐乐 魏
Keyword(s):  
Linear Groups ◽  
Two Dimension ◽  
Projective Linear Groups

scholarly journals PROJECTIVE LINEAR GROUPS AS MAXIMAL SYMMETRY GROUPS

2008 ◽  
Vol 50 (1) ◽  
pp. 83-96 ◽  
Author(s):  
ANNA TORSTENSSON
Keyword(s):  
Symmetry Group ◽  
Hyperbolic Manifold ◽  
Three Dimensional ◽  
Maximal Order ◽  
Linear Groups ◽  
Symmetry Groups ◽  
Maximal Symmetry ◽  
Projective Linear Groups

AbstractA maximal symmetry group is a group of isomorphisms of a three-dimensional hyperbolic manifold of maximal order in relation to the volume of the manifold. In this paper we determine all maximal symmetry groups of the typesPSL(2,q) andPGL(2,q). Depending on the primepthere are one or two such groups withq=pkandkalways equals 1, 2 or 4.

scholarly journals Projective linear groups as automorphism groups of chiral polytopes

2017 ◽  
Vol 108 (2) ◽  
pp. 675-702
Author(s):  
Dimitri Leemans ◽  
Jérémie Moerenhout ◽  
Eugenia O’Reilly-Regueiro
Keyword(s):  
Automorphism Groups ◽  
Linear Groups ◽  
Chiral Polytopes ◽  
Projective Linear Groups

scholarly journals A characterisation of PSL2(Zþλ) and PGL2(Zþλ)

1968 ◽  
Vol 8 (3) ◽  
pp. 523-543 ◽  
Author(s):  
G. E. Wall
Keyword(s):  
Finite Field ◽  
Prime Power ◽  
Cyclic Subgroup ◽  
Residue Class ◽  
Linear Groups ◽  
Cyclic Subgroups ◽  
Even Order ◽  
Residue Class Ring ◽  
Projective Linear Groups ◽  
Class Ring

Let Fq denote the finite field with q elements, Zm the residue class ring Z/mZ. It is known that the projective linear groups G = PSL2(Fq) and PGL2(Fq) (q a prime-power ≥ 4) are characterised among finite insoluble groups by the property that, if two cyclic subgroups of G of even order intersect non-trivially, they generate a cyclic subgroup (cf. Brauer, Suzuki, Wall [2], Gorenstein, Walter [3]). In this paper, we give a similar characterisation of the groups G = PSL2 (Zþt+1) and PGL2 (Zþt+1) (p a prime ≥ 5, t ≥ 1).

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