✦ LIBER ✦

A New Maximal Subgroup of the Monster

✍ Scribed by P.E. Holmes; R.A. Wilson

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 108 KB
Volume: 251
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.9037

No coin nor oath required. For personal study only.

✦ Synopsis

We use our computer construction of the Monster sporadic simple group to find a new maximal subgroup PGL 2 (29). In particular, we prove containment of L 2 (29) in , thereby answering a long-standing open question.

📜 SIMILAR VOLUMES

Elementary Abelian 3-Subgroups of the Mo

Elementary Abelian 3-Subgroups of the Monster

✍ Thomas M. Richardson 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 297 KB

We classify the maximal elementary abelian 3-subgroups of the Monster simple group. There are 17 conjugacy classes of such subgroups. Fifteen of the classes have groups of order 3 7 , and the other classes have groups of order 3 6 and 3 8 . The classification uses the construction of 3-local subgrou

Automorphisms of Models of True Arithmet

Automorphisms of Models of True Arithmetic: Subgroups which Extend to a Maximal Subgroup Uniquely

✍ Henryk Kotlarski; Bożena Piekart 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 420 KB

## Abstract We show that if __M__ is a countable recursively saturated model of True Arithmetic, then __G__ = Aut(__M__) has nonmaximal open subgroups with unique extension to a maximal subgroup of Aut(__M__). Mathematics Subject Classification: 03C62, 03C50.

A Note on the δ-length of Maximal Subgro

A Note on the δ-length of Maximal Subgroups in Finite Soluble Groups

✍ A. Ballester-Bolinches; M. D. Pérez-Ramos 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 253 KB

A formation is a class 3 of groups which is closed under homomorphic images and is such that each group G has a unique smallest normal subgroup H with factor group in 5. This uniquely determined normal subgroup of G is called the 8-residual subgroup of G and will be denoted here by G,. The formatio

Maximal Integral Forms of the Algebraic

Maximal Integral Forms of the Algebraic Group G2 Defined by Finite Subgroups

✍ Arjeh M. Cohen; Gabriele Nebe; Wilhelm Plesken 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 454 KB

We coin the notation maximal integral form of an algebraic group generalizing Gross' notion of a model. We extend the mass formula given by Gross to our context. For the finite Lie primitive subgroups of G 2 there are unique maximal integral forms defined by them.

Sylow Subgroups Which Are Maximal in the

Sylow Subgroups Which Are Maximal in the Universal Locally Finite Group of Philip Hall

✍ Marianna Dalle Molle 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 104 KB

For every prime p, we construct a subgroup of Philip Hall's universal locally finite group which is both maximal and a p-group. This provides an example of a simple locally finite group with a maximal subgroup which is locally nilpotent. ᮊ 1999 Academic Press G theme to a locally finite group G, fin

Automorphisms of Models of True Arithmet

Automorphisms of Models of True Arithmetic: More on Subgroups which Extend to a Maximal One Uniquely

✍ Henryk Kotlarski; Bożena Piekart 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 239 KB

Continuing the earlier research in [14] we give some more information about nonmaximal open subgroups of G = Aut(M) with unique maximal extension, where M is a countable recursively saturated model of True Arithmetic.