Independent generating sets and geometries for symmetric groups

DOI10.1016/S0021-8693(02)00550-1zbMath1030.20002MaRDI QIDQ1858296

Peter J. Cameron, Philippe Cara

Publication date: 12 February 2003

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

symmetric groupscoset geometriesindependent generating sets

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Combinatorial aspects of finite geometries (05B25) Buildings and the geometry of diagrams (51E24) Symmetric groups (20B30)

Related Items (20)

The largest size of a minimal generating set of a finite group. ⋮ Minimal generating sets of maximal size in finite monolithic groups. ⋮ A generalization of the Burnside basis theorem. ⋮ String C-groups as transitive subgroups of \(\operatorname{S}_n\) ⋮ Finite groups satisfying the independence property ⋮ Large minimal invariable generating sets in the finite symmetric groups ⋮ Rank properties of the semigroup of endomorphisms over Brandt semigroup ⋮ The independence graph of a finite group ⋮ Unnamed Item ⋮ Polytopes of high rank for the symmetric groups ⋮ Rank properties of the semigroup reducts of affine near-semirings over Brandt semigroups ⋮ On the replacement property for PSL(2, p ) ⋮ An extension of the classification of high rank regular polytopes ⋮ Maximal subgroups of finite soluble groups in general position ⋮ Bounding the maximal size of independent generating sets of finite groups ⋮ String C-group representations of alternating groups ⋮ Minimal invariable generating sets ⋮ String C-group representations of almost simple groups: A survey ⋮ On quantum vs. classical probability ⋮ On the maximal size of independent generating sets of \(\text{PSL}_2(q)\)

Uses Software

• GAP

Cites Work

• Buildings of spherical type and finite BN-pairs
• Some properties of inductively minimal geometries
• Maximal independent generating sets of the symmetric group
• On the number of inductively minimal geometries
• Unnamed Item
• Unnamed Item

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