Related papers: Classification of subgroups 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 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.

The classification of the maximal subgroups of the Monster $\mathbf{M}$ is believed to be complete subject to an unpublished result of Holmes and Wilson asserting that $\mathbf{M}$ has no maximal subgroups that are almost simple with socle…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

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…

There exists no bad group (in the sense of Gregory Cherlin), namely any simple group of Morley rank 3 is isomorphic to PSL2(K) for an algebraically closed field K.

We show that a group with a presentation satisfying the C(6) small cancellation condition cannot contain a subgroup isomorphic to F_2 X F_2.

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 classify all corefree fusion systems on a Sylow $3$-subgroup of the sporadic groups $\mathrm{Fi}_{22}$, $\mathrm{Fi}_{23}$ and $\mathrm{B}$. We show that the $3$-group in each case does not support any exotic fusion systems. This is the…

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…

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…

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 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…

We study the parafermionization of the Monster CFT with respect to its $\mathbb{Z}_{pA}$ subgroups, with $p$ an odd prime. Under certain assumptions, we show that the parafermionization is equal to a non-invertible gauging of…

In this paper we characterize the elements of PSL(2,Z), as a subgroup of Thompson group T, in the language of reduced tree pair diagrams and in terms of piecewise linear maps as well. Actually, we construct the reduced tree pair diagram for…

We show that Gromov's monsters arising from i.i.d. random labellings of expanders (that we call random Gromov's monsters) have linear divergence along a subsequence, so that in particular they do not contain Morse quasigeodesics, and they…

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…

In this short note we prove that the finite non-abelian simple groups PSL(2,q), where q = 5,7, are determined by their posets of classes of isomorphic subgroups. In particular, this disproves the conjecture in the end of [5].

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 right transversals of H in G is two.