相关论文: There is no Sz(8) in the Monster

We prove that the Monster does not contain any subgroup isomorphic to PSL_2(27).

We describe computer calculations that were used in 2016 to classify subgroups of the Monster isomorphic to $PSL_2(8)$, containing $7B$-elements. It turns out that there is no such $PSL_2(8)$ in the Monster. These calculations confirm…

As a contribution to an eventual solution of the problem of determination of the maximal subgroups of the Monster we show that there is a unique conjugacy class of subgroups isomorphic to $PSU_3(8)$. The argument depends on some…

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…

The classification of the maximal subgroups of the Monster $\mathbf{M}$ is believed to be complete subject to an unpublished result of Holmes and Wilson asserting that $\mathbf{M}$ has no maximal subgroups that are almost simple with socle…

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 give a new computer-assisted proof of the classification of maximal subgroups of the simple group ${}^2E_6(2)$ and its extensions by any subgroup of the outer automorphism group $S_3$. This is not a new result, but no earlier proof…

Seysen's Python package mmgroup provides functionality for fast computations within the sporadic simple group $\mathbb{M}$, the Monster. The aim of this work is to present an mmgroup database of maximal subgroups of $\mathbb{M}$: for each…

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…

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…

In this paper, we prove that there does not exist a subgroup H of a finite group G such that the number of isomorphism classes of right transversals of H in G is two.

We employ the recently developed hybrid and mmgroup computational models for groups to calculate the character table of $N(\rm{2B}^5) \cong 2^{5+10+20}.( \rm{S}_3 \times \rm{L}_5 {2} )$, a maximal subgroup of the Monster sporadic simple…

We establish the existence of maximal subgroups of various diferent natures in SL(n,Z). In particular, we prove that there are continuously many maximal subgroups, we provide a maximal subgroup whose action on the projective space has no…

In this paper we prove that there does not exist a subgroup $H$ of a finite group $G$ such that the number of isomorphism classes of normalized right transversals of $H$ in $G$ is four.

We prove the existence and uniqueness of a new maximal subgroup of the algebraic group of type $E_8$ in characteristic $3$. This has type $F_4$, and was missing from previous lists of maximal subgroups produced by Seitz and Liebeck--Seitz.…

Consider $\mathbb{Z}/8\mathbb{Z}\oplus \mathbb{Z}/2\mathbb{Z}$, and the subgroup generated by $(2,1)$, it is a subgroup isomorphic to $\mathbb{Z}/4\mathbb{Z}$. If my theorem holds, it must contained in a cyclic group generated by some…

We determine the conjugacy class fusion from certain maximal subgroups of the Monster to the Monster, to justify the addition of these data to the Character Table Library in the computational algebra system GAP. The maximal subgroups in…

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…

A systematic study of maximal subgroups of the sporadic simple groups began in the 1960s. The work is now almost complete, only a few cases in the Monster remaining outstanding. We give a survey of results obtained, and methods used, over…

The question of existence of a maximal subgroup in the multiplicative group D* of a division algebra D finite dimensional over its center F is investigated. We prove that if D* has no maximal subgroup, then deg(D) is not a power of 2,…