Related papers: Enumeration of Nilpotent Loops by Orbit Counting

We define an abelian loop on a set $S$ consisting of 1 and all odd prime numbers with an operation $\bullet$, where for $a,b$ $\in$ $S$, $a$ $ \bullet$ $b$ is the smallest element of $S$ strictly larger than $|a-b|$. We use theorems and…

We estimate size of recurrence of an action of a nilpotent group by homeomorphisms of a compact space for polynomial mappings into a nilpotent group form the partial semigroup $(\mathcal{P}_{f}(\mathbb{N}),\uplus)$. To do this we have used…

Let $R(r,n)$ be the $r$th order Reed-Muller code of length $2^n$. The affine linear group $\text{AGL}(n,\Bbb F_2)$ acts naturally on $R(r,n)$. We derive two formulas concerning the number of orbits of this action: (i) an explicit formula…

We construct Morse homology groups associated with any regular function on a smooth complex algebraic variety, allowing singular and non-compact critical loci. These groups are generated by critical points of a certain large pertubation of…

In this paper we consider the problem of classification of nilpotent orbits for the pseudo-quaternionic coset manifolds U/H* obtained in the time-like dimensional reduction of N = 2 supergravity models based on homogeneous symmetric special…

We calculate the number of the isomorphism class of the finite flat models over the ring of integers of an absolutely ramified $p$-adic field of constant group schemes of rank two over finite fields, by counting the rational points of a…

We consider the conjugation-action of the Borel subgroup of the symplectic or the orthogonal group on the variety of nilpotent complex elements of nilpotency degree $2$ in its Lie algebra. We translate the setup to a…

We report on some computations with nilpotent orbits in simple Lie algebras of exceptional type within the SLA package of GAP4. Concerning reachable nilpotent orbits our computations firstly confirm the classification of such orbits in Lie…

Let $G$ be an adjoint algebraic group of type $B$, $C$, or $D$ over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the Lie algebra of $G$. In particular, for orthogonal Lie algebras in…

In this paper, we give a characterization of hypercyclic abelian affine group G. If G is finitely generated, this characterization is explicit. We prove in particular that no abelian group generated by n affine maps on C^n has a dense…

We give a characterization of hypercyclic using (locally hypercyclic) of semigroup G of affine maps of C^n. We prove the existence of a G-invariant open subset of C^n in which any locally hypercyclic orbit is dense in C^n.

Given a nilpotent orbit O of a real, reductive algebraic group, a necessary condition is given for the existence of a tempered representation pi such that O occurs in the wave front cycle of pi. The coefficients of the wave front cycle of a…

In this paper, we study affine transformations on tori, nilmanifolds and compact abelian groups. For these systems, we show that an equivalent condition for zero entropy is the orbit closure of each point has a nice structure. To be…

In this paper we continue the program of the classification of nilpotent orbits using the approach developed in arXiv:1107.5986, within the study of black hole solutions in D=4 supergravities. Our goal in this work is to classify static,…

Let $S$ be a class of groups and let $f_S (n)$ be the number of isomorphism classes of groups in $S$ of order $n$. Let $f(n)$ count the number of groups of order $n$ up to isomorphism. The asymptotic bounds for $f(n)$ behave differently…

It is known that with precision till isomorphism that only and only loops $M(F) = M_0(F)/<-1>$, where $M_0(F)$ denotes the loop, consisting from elements of all matrix Cayley-Dickson algebra $C(F)$ with norm 1, and $F$ be a subfield of…

Let $p$ be a prime and $G$ a subgroup of $GL_d(p)$. We define $G$ to be $p$-exceptional if it has order divisible by $p$, but all its orbits on vectors have size coprime to $p$. We obtain a classification of $p$-exceptional linear groups.…

We study when kernels of inflation maps associated to extraspecial p-groups in stable group cohomology are generated by their degree two components. This turns out to be true if the prime is large enough compared to the rank of the…

Let $G$ be a finite solvable group, given through a refined consistent polycyclic presentation, and $\alpha$ an automorphism of $G$, given through its images of the generators of $G$. In this paper, we discuss algorithms for computing the…

In this paper, we consider covers of finite groups by centralizers of elements. We show that the set of centralizers that are maximal under the partial ordering form a cover of the group. We also show that the set of centralizers that are…