相关论文: What is the monster?
We explain a conjecture relating the monster simple group to an algebraic variety that was discovered in a non-monstrous context.
It is well known that Tarski monster groups of exponent~3 do not exist. Traditional proofs rely on deep structural results, such as the restricted Burnside problem, properties of the free Burnside group, or Engel-type identities, and…
We prove the correctness of the character table of the sporadic simple Baby Monster group that is shown in the Atlas of Finite Groups.
This article is a short and elementary introduction to the monstrous moonshine aiming to be as accessible as possible. I first review the classification of finite simple groups out of which the monster naturally arises, and features of the…
We present a modular function-based approach to explaining, for primes larger than 3, the exponents that appear in the prime decomposition of the order of the monster finite simple group.
We discuss ways in which the black-box model for computation is or is not applicable to the Monster sporadic simple group. Conversely, we consider whether methods of computation in the Monster can be generalised to other situations, for…
A left orderable monster is a finitely generated left orderable group all of whose fixpoint-free actions on the line are proximal: the action is semiconjugate to a minimal action so that for every bounded interval $I$ and open interval $J$,…
We use uniqueness of a VOA (vertex operator algebra) extension of $(V_{EE_8}^+)^3$ to a Moonshine type VOA to give a new existence proof of a finite simple group of Monster type. The proof is relatively direct. Our methods depend on VOA…
We determine the order of the largest of the twenty-six sporadic simple groups known as the Monster, using a straightforward computational approach. The Monster is here defined as a subgroup of the symmetry group of the 196884-dimensional…
As a contribution to an eventual solution of the problem of the determination of the maximal subgroups of the Monster we show that there is no subgroup isomorphic to Sz(8). The proof is largely, though not entirely, computer-free.
Together with their 1988 construction of the monster vertex algebra $V^\natural$, Frenkel, Lepowsky, and Meurman showed that the largest sporadic simple group, known as the Fischer-Griess monster, forms the symmetry group of an infinite…
This is brief and hopefully friendly, with basic notions, a few different perspectives, and references with more information in various directions.
The commencement of monstrous moonshine is a connection between the largest sporadic simple group---the monster---and complex elliptic curves. Here we explain how a closer look at this connection leads, via the Thompson group, to recently…
We show the details of certain computations that are used in the paper "Verification of the conjugacy classes and ordinary character table of the Monster".
We review the construction of monsters in classical general relativity. Monsters have finite ADM mass and surface area, but potentially unbounded entropy. From the curved space perspective they are objects with large proper volume that can…
Axial algebras of Monster type are a class of non-associative algebras which generalise the Griess algebra, whose automorphism group is the largest sporadic simple group, the Monster. The $2$-generated algebras, which are the building…
We prove that the Monster does not contain any subgroup isomorphic to PSL_2(27).
A monster is an automaton in which every function from states to states is represented by at least one letter. A modifier is a set of functions allowing one to transform a set of automata into one automaton. We revisit some language…
The classification of the maximal subgroups of the Monster $\mathbf{M}$ is believed to be complete subject to an unpublished result of Holmes and Wilson asserting that $\mathbf{M}$ has no maximal subgroups that are almost simple with socle…
The classification of the maximal subgroups of the Monster $\mathbf{M}$ is a long-standing problem in finite group theory. According to the literature, the classification is complete apart from the question of whether $\mathbf{M}$ contains…