On generators and representations of the sporadic simple groups

2012/10/23 by Di Martino, L., Pellegrini, M. A., Zalesski, A. E. · 3 citations
#20C15 #20C20 #20C34 #20C40 #20F05 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1210.6152

Abstract

In this paper we determine the irreducible projective representations of sporadic simple groups over an arbitrary algebraically closed field F, whose image contains an almost cyclic matrix of prime-power order. A matrix M is called cyclic if its characteristic and minimum polynomials coincide, and we call M almost cyclic if, for a suitable a in F, M is similar to diag(a Id_h, M₁), where M₁ is cyclic and 0 <= h <= n. The paper also contains results on the generation of sporadic simple groups by minimal sets of conjugate elements.

Cited by

• Unisingular representations of rank 1 finite simple groups of Lie type
• Linear groups of alternating type containing non-scalar elements with all but one eigenvalues of multiplicity 1
• On generation by triality automorphisms

Related

• Almost cyclic elements in Weil representations of finite classical groups
• The (2,p)-generation of sporadic simple groups
• An identification theorem for the sporadic simple groups F₂ and M(23)
• Matrices of simple spectrum in irreducible representations of cyclic extensions of simple algebraic groups
• Conjugate generation of sporadic almost simple groups