Finite subgroups of G2,(c)

DOI10.1080/00927878308822857zbMath0517.20020OpenAlexW2149146864MaRDI QIDQ3665317

Arjeh M. Cohen, David B. Wales

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1080/00927878308822857

zbMATH Keywords

automorphism groupsemi-direct productprimitive groupsconjugacy classes of finite subgroupsspecial unitary groupimprimitive groupscomplex Lie groupfinite automorphism groups of real octavesLie group of type G2real Cayley numbersreal quaternion division algebra

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Discrete subgroups of Lie groups (22E40) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Representations of groups as automorphism groups of algebraic systems (20F29)

Related Items (20)

The groupL(2 61) embeds in t h e Lie group of typeE₈ ⋮ Chevalley groups of type \(G_ 2\) as the group of a trilinear form ⋮ On an explicit isomorphism of standard level-one modules for \(\hat D_{4n}\) ⋮ Basic conjugacy theorems for \(G_ 2\) ⋮ On the automorphism groups of certain hypersurfaces II ⋮ \(G_{2}\) and some exceptional Witt vector identities ⋮ Polyhedral groups in ⋮ Zero-one generation laws for finite simple groups ⋮ Kostant's conjecture and L₂(q) invariant theory in the rank two lie groups ⋮ Spectral measures for G2, II: Finite subgroups ⋮ \(G_2\) and hypergeometric sheaves ⋮ On Non-Generic Finite Subgroups of Exceptional Algebraic Groups ⋮ Embeddings of the group \(L(2,13)\) in groups of Lie type \(E_ 6\) ⋮ Conjugacy of \(\text{Alt}_5\) and \(\text{SL}(2,5)\) subgroups of \(E_6(\mathbb{C})\), \(F_4(\mathbb{C})\), and a subgroup of \(\mathbb{E}_8(\mathbb{C})\) of type \(A_2E_6\) ⋮ Maximal integral forms of the algebraic group \(G_2\) defined by finite subgroups ⋮ Notes on \(G_{2}\), determinants, and equidistribution ⋮ Unnamed Item ⋮ Finite simple groups which projectively embed in an exceptional Lie group are classified! ⋮ The Freund–Rubin coset, textures and group theory ⋮ Embeddings of \(U_ 3(8)\), \(Sz(8)\) and the Rudvalis group in algebraic groups of type \(E_ 7\)

Cites Work

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• Blocks with cyclic defect groups
• Über endliche lineare Gruppen von Primzahlgrad. (On finite linear groups of prime number degree)
• Finite linear groups of degree seven. II
• Blocks of modular representations
• Sur certaines sous-groupes des groupes de Lie compacts
• Investigations on group characters
• On groups whose orders contain a prime number to the first power
• Integral Cayley numbers
• Klassifizierung der alternierenden Gröszen dritten Grades in 7 Dimensionen
• On Groups Whose Order Contains a Prime Number to the First Power I
• On simple groups of finite order. I

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