On Generators and Representations of the Sporadic Simple Groups

DOI10.1080/00927872.2012.729629zbMath1298.20043arXiv1210.6152OpenAlexW2003550889MaRDI QIDQ5409822

Marco Antonio Pellegrini, Lino Di Martino, Alexander E. Zalesskij

Publication date: 14 April 2014

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

Full work available at URL: https://arxiv.org/abs/1210.6152

zbMATH Keywords

sporadic simple groupsirreducible representationseigenvalue multiplicitiesgenerations by conjugates

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Linear algebraic groups over finite fields (20G40) Simple groups: sporadic groups (20D08) Generators, relations, and presentations of groups (20F05) Representations of sporadic groups (20C34) Projective representations and multipliers (20C25)

Related Items (10)

On the sharp Baer-Suzuki theorem for the \(\pi \)-radical: sporadic groups ⋮ Groups with a \(p\)-element acting with a single non-trivial Jordan block on a simple module in characteristic \(p\) ⋮ Almost cyclic elements in Weil representations of finite classical groups ⋮ On generations by conjugate elements in almost simple groups with socle \(^2 F_4(q^2)'\) ⋮ The (p,q,r)-generations of the alternating group A_11 ⋮ Unnamed Item ⋮ On the ranks of the alternating group \(A_n\) ⋮ On the ranks of Fischer group $Fi_{24}^{,prime}$ and the Baby Monster group $mathbb{B}$ ⋮ Almost cyclic elements in cross-characteristic representations of finite groups of Lie type ⋮ Baer-Suzuki theorem for the \(\pi \)-radical

Uses Software

• GAP

Cites Work

• Unnamed Item
• The covering numbers of the sporadic simple groups
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• Collineation groups generated by homologies of order greater than 2
• \((p,q,r)\)-generations of the smallest Conway group \(Co_ 3\)
• Generation of finite almost simple groups by conjugates.
• UNIPOTENT ELEMENTS IN REPRESENTATIONS OF FINITE GROUPS OF LIE TYPE
• The Finite Simple Groups
• LINEAR GROUPS GENERATED BY TRANSVECTIONS
• Linear Groups with Orders Having Certain Large Prime Divisors
• Minimal Polynomials and Eigenvalues of p -Elements in Representations of Quasi-Simple Groups with a Cyclic Sylow p -Subgroup
• The Minimal Degrees of Faithful Representations of the Sporadic Simple Groups and their Covering Groups

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