Related papers: Indecomposable racks of order p^2

Using the classification of transitive groups we classify indecomposable quandles of size <36. This classification is available in Rig, a GAP package for computations related to racks and quandles. As an application, the list of all…

Rank 2 indecomposable arithmetically Cohen-Macaulay bundles E on a nonsingular cubic surface X in P^3 are classified, by means of the possible forms taken by the minimal graded free resolution of E over P^3. The admissible values of the…

We classify indecomposable aCM bundles of rank $2$ on the del Pezzo threefold of degree $7$ and analyze the corresponding moduli spaces.

We use the inflation-restriction sequence and a result of Etingof and Gra\~na on the rack cohomology to give a explicit description of 2-cocycles of finite indecomposable quandles with values in an abelian group. Several applications are…

We characterize the finite groups of minimal order that admit an irreducible complex character of degree $p$ or $p^2$, where $p$ is a prime.

We establish a canonical correspondence between connected quandles and certain configurations in transitive groups, called quandle envelopes. This correspondence allows us to efficiently enumerate connected quandles of small orders, and…

This paper concerns finite groups of class (at most) two and of odd prime exponent $p$. Such a group is called special if the center lies within its derived group. Every group of class 2 and exponent $p$ can be uniquely expressed as the…

A group of order $p^n$ ($p$ prime) has an indecomposable polynomial invariant of degree at least $p^{n-1}$ if and only if the group has a cyclic subgroup of index at most $p$ or it is isomorphic to one of two particular groups of small…

We classify the finite dimensional irreducible representations of affine Hecke algebras of type B_2 with unequal parameters.

A quandle will be called quasi-affine, if it embeds into an affine quandle. Our main result is a characterization of quasi-affine quandles, by group-theoretic properties of their displacement group, by a universal algebraic condition coming…

We classify and construct irreducible completely splittable representations of affine and finite Hecke-Clifford algebras over an algebraically closed field of characteristic not equal to 2.

Two finite Alexander quandles with the same number of elements are isomorphic iff their Z[t,t^-1]-submodules Im(1-t) are isomorphic as modules. This yields specific conditions on when Alexander quandles of the form Z_n[t,t^-1]/(t-a) where…

We classify all non-simple connected quandles of size $pq$ and $4p$ where $p,q$ are primes, as a special family of locally strictly simple quandles (i.e. quandles for which all proper subquandles are strictly simple). In particular we…

We define a new class of racks, called finitely stable racks, which, to some extent, share various flavors with Abelian groups. Characterization of finitely stable Alexander quandles is established. Further, we study twisted rack dynamical…

For finite p-groups P of class 2 and exponent p the following are invariants of fully refined central decompositions of P: the number of members in the decomposition, the multiset of orders of the members, and the multiset of orders of…

In this paper we provide an alternative characterization of finite simply connected quandles involving only cocycles with values in abelian groups of prime size. As a corollary of such a characterization and the classification of connected…

A rack of order $n$ is a binary operation $\rack$ on a set $X$ of cardinality $n$, such that right multiplication is an automorphism. More precisely, $(X,\rack)$ is a rack provided that the map $x\mapsto x\rack y$ is a bijection for all…

We prove that for any prime number $p$, every finite non-abelian $p$-group $G$ of class 2 has a noninner automorphism of order $p$ leaving either the Frattini subgroup $\Phi(G)$ or $\Omega_1(Z(G))$ elementwise fixed.

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

We develop some general ideas to study connected quandles of prime power size and we classify non-affine connected quandles of size $p^3$ for $p>3$, using a combination of group theoretical and universal algebraic tools. As a byproduct we…