相关论文: Centralisers of Involutions in Black Box Groups

The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…

The main purpose of this paper is to develop new algorithms for computing invariant rings in a general setting. This includes invariants of nonreductive groups but also of groups acting on algebras over certain rings. In particular, we…

This paper investigates centralizers and twisted centralizers in degenerate and non-degenerate Clifford (geometric) algebras. We provide an explicit form of the centralizers and twisted centralizers of the subspaces of fixed grades,…

There is a well-known classification of conjugacy classes of involutions in finite Coxeter groups, in terms of subsets of nodes of their Coxeter graphs. In many cases, the product of an involution with the longest element is again an…

In this paper we study the existence of at least one non-inner automorphism of order p in a finite normally constrained p-group when p is an odd prime.

A recurring theme in finite group theory is understanding how the structure of a finite group is determined by the arithmetic properties of group invariants. There are results in the literature determining the structure of finite groups…

We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural…

In general the endomorphisms of a non-abelian group do not form a ring under the operations of addition and composition of functions. Several papers have dealt with the ring of functions defined on a group which are endomorphisms when…

Neural classifiers are non linear systems providing decisions on the classes of patterns, for a given problem they have learned. The output computed by a classifier for each pattern constitutes an approximation of the output of some unknown…

We define a new class of countable groups, which are defined by its action on the set of monotonic numberings (diagrams) of an arbitrary finite or countable partial ordered set (poset). These groups are generated by the set of involutions?…

It is known that that the centralizer of a matrix over a finite field depends, up to conjugacy, only on the type of the matrix, in the sense defined by J. A. Green. In this paper an analogue of the type invariant is defined that in general…

The article is about a "desingularization principle" common to various canonical desingularization algorithms in characteristic zero, and the roles played by the exceptional divisors in the underlying local construction. We compare…

We describe the centralizer of irreducible representations from a finitely generated group $\Gamma$ to $PSL(p,\mathbb{C})$ where $p$ is a prime number. This leads to a description of the singular locus (the set of conjugacy classes of…

We report an ongoing work on clustering algorithms for complex roots of a univariate polynomial $p$ of degree $d$ with real or complex coefficients. As in their previous best subdivision algorithms our root-finders are robust even for…

Let $G$ be a finite group having a normal $p$-subgroup $N$ that contains its centralizer $\text{C}_{G}(N)$, and let $R$ be a $p$-adic ring. It is shown that any finite $p$-group of units of augmentation one in $RG$ which normalizes $N$ is…

We compute the Whitehead groups of the associative rings in a class which includes (twisted) formal power series rings and the augmentation localizations of group rings and polynomial rings. For any associative ring A, we obtain an…

We construct here the first known examples of non-split sharply 2-transitive groups of bounded exponent in odd positive characteristic for every large enough prime $p \equiv 3 \pmod{4}$. In fact, we show that there are countably many…

We characterize all finite p-groups G of order p^n(n\leq 6), where p is a prime for n\leq 5 and an odd prime for n = 6, such that the center of the inner automorphism group of G is equal to the group of central automorphisms of G.

In this note, we verify that several fundamental results from the theory of representations of reductive $p$-adic groups, extend to finite central extensions of these groups.

We present the ideas behind an algorithm to compute normalizers of primitive groups with non-regular socle in polynomial time. We highlight a concept we developed called permutation morphisms and present timings for a partial implementation…