Related papers: Factorization of finite simple groups

Let $f(x)=x^8+ax^4+b \in \mathbb{Q}[x]$ be an irreducible polynomial where $b$ is a square. We give a method that completely describes the factorization patterns of a linear resolvent of $f(x)$ using simple arithmetic conditions on $a$ and…

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

We prove that different expressions of the same exceptional unimodal singularity are orbifold equivalent. As in our previous paper, the matrix factorizations proving these orbifold equivalences depend again on certain parameters satisfying…

We prove that the only finite factor-representations of the Higman-Thompson groups $\{F_{n,r}\}$, $ \{G_{n,r}\}$ are the regular representations and scalar representations arising from group abelianizations. As a corollary, we obtain that…

In this paper, we will prove some sufficient conditions for the solvability of groups.

In this note we prove that every finite collection of connected algebraic subgroups of the group of triangular automorphisms of the affine space generates a connected solvable algebraic subgroup.

We say that a class of finite structures for a finite first-order signature is $r$-compressible if each structure $G$ in the class has a first-order description of size at most $O(r(|G|))$. We show that the class of finite simple groups is…

We show that every (not necessarily saturated) fusion system can be realized as a full subcategory of the fusion system of a finite group. This result extends our previous work \cite{Park2010} and complements the related result…

We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Moebius group of the projective line. Since the general proof is very simple but not…

We show that an elementary proof of Fermat's Last Theorem (FLT) exists. Our paper also extends the scope of FLT from integers to all rational numbers.

We show that the subgroup lattice of any finite group satisfies Frankl's Union-Closed Conjecture. We show the same for all lattices with a modular coatom, a family which includes all supersolvable and dually semimodular lattices. A common…

Following the works by Lin et al. (Circuits Syst. Signal Process. 20(6): 601-618, 2001) and Liu et al. (Circuits Syst. Signal Process. 30(3): 553-566, 2011), we investigate how to factorize a class of multivariate polynomial matrices. The…

In this note we study the finite groups whose subgroup lattices are dismantlable.

We prove that every slim double Lie groupoid with proper core action is completely determined by a factorization of a certain canonically defined "diagonal" Lie groupoid.

We show that every countable group embeds in a group of type $FP_2$.

We present a new proof, which is independent of the finite simple group classification and applies also to infinite groups, that quasiprimitive permutation groups of simple diagonal type cannot be embedded into wreath products in product…

In [2] a new factorization for infinite Hessenberg banded matrices was introduced. In this note we prove that this kind of factorization can also be used for finite matrices. In addition, a new method for solving banded linear systems is…

We prove that Riemannian foliations on complete contractible manifolds have a closed leaf, and that all leaves are closed if one closed leaf has a finitely generated fundamental group. Under additional topological or geometric assumptions…

Let R be a finite unitary ring whose group of units is not solvable but all groups of units of all its proper subrings are solvable. In this paper we classify these rings and show that all finite rings of order $p^n$ for $n < 5$ and some of…

If $R$ is a rational map, the Main Result is a uniformization Theorem for the space of decompositions of the iterates of $R$. Secondly, we show that Fatou conjecture holds for decomposable rational maps.