Related papers: A Frobenius group analog for Camina triples
The problem of finding the number of ordered commuting tuples of elements in a finite group is equivalent to finding the size of the solution set of the system of equations determined by the commutator relations that impose commutativity…
We present a procedure to enumerate the whole set of numerical semigroups with a given Frobenius number F, S(F). The methodology is based on the construction of a partition of S(F) by a congruence relation. We identify exactly one…
We define a Frobenius algebra over fusion categories of the form Rep$(G)\boxtimes$Rep$(G)$ which generalizes the diagonal subgroup of $G\times G$. This allows us to extend field theoretical constructions which depend on the existence of a…
We present a new class of extended affine Weyl groups $\widetilde{W}^{(k,k+1)}(A_l)$ for $1\leq k <l$ and obtain an analogue of Chevalley-type theorem for their invariants. We further show the existence of Frobenius manifold structures on…
We study adjoint and Frobenius pairs of functors, equivalences, and the Picard group for corings.
An $\mathcal{A}$-semigroup is a numerical semigroup without consecutive small elements. This work generalizes this concept to finite-complement submonoids of an affine cone $\mathcal{C}$. We develop algorithmic procedures to compute all…
Manin triple construction of N=4 superconformal field theories is considered. The correspondence between quasi Frobenius finite-dimensional Lie algebras and N=4 superconformal field theories is established.
In this paper, we introduce and study the numerical semigroups generated by $\{a_1, a_2, \ldots \} \subset \mathbb{N}$ such that $a_1$ is the repunit number in base $b > 1$ of length $n > 1$ and $a_i - a_{i-1} = a\, b^{i-2},$ for every $i…
A group G is almost cyclic if there is an element x in G, such that for all g in G, there is an element y in G and an integer n with ygy^{-1} = x^n (that is, every element is conjugate to some power of x). W. Ziller asked whether there are…
Let $V$ be a finite rank vector space over a perfect field of characteristic $p>0$, and let $G$ be a finite subgroup of $\operatorname{GL}(V)$. If $V$ is a permutation representation of $G$, or more generally a monomial representation, we…
If $m \in \mathbb{N}$ and $A$ is a finite subset of $\bigcup_{k \in \mathbb{N} \setminus \{0,1\}} \{1,\ldots,m-1\}^k$, then we denote by \begin{align*} \mathscr{C}(m,A) = \left\{S\in \mathscr{S}_m \mid s_1+\cdots+s_k-m \in S \mbox{ if }…
We give an analog of Frobenius' theorem about the factorization of the group determinant on the group algebra of finite abelian groups and we extend it into dihedral groups and generalized quaternion groups. Furthermore, we describe the…
Fixed two positive integers m and e, some algorithms for computing the minimal Frobenius number and minimal genus of the set of numerical semigroups with multiplicity m and embedding dimension e are provided. Besides, the semigroups where…
A finite transitive permutation group is said to be 3/2-transitive if all the nontrivial orbits of a point stabilizer have the same size greater than 1. Examples include the 2-transitive groups, Frobenius groups and several other less…
The groups QF, QT, and QV are groups of quasi-automorphisms of the infinite binary tree. Their names indicate a similarity with Thompson's well-known groups F, T, and V. We will use the theory of diagram groups over semigroup presentations…
Frobenius problem and its many generalizations have been extensively studied in several areas of mathematics. We study semigroups of totally positive algebraic integers in totally real number fields, defining analogues of the Frobenius…
A Lie version of Turaev's $\overline{G}$-Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a \textit{$\frak{g}$-quasi-Frobenius Lie algebra} for…
Let $G$ be a finite group and, for a given complex character $\chi$ of $G$, let ${\mathbb{Q}}(\chi)$ denote the field extension of ${\mathbb{Q}}$ obtained by adjoining all the values $\chi(g)$, for $g\in G$. The group $G$ is called…
We study co-Frobenius and more generally Quasi-co-Frobenius corings over arbitrary baserings and over PF baserings in particular. We generalize some results about (Quasi-) co-Frobenius coalgebras to the case of non-commutative base rings…
A finite group $P$ is said to be \emph{primary} if $|P|=p^{a}$ for some prime $p$. We say a primary subgroup $P$ of a finite group $G$ satisfies the \emph{Frobenius normalizer condition} in $G$ if $N_{G}(P)/C_{G}(P)$ is a $p$-group provided…