arXiv subjects
Publications and source records attributed to Layla Sorkatti.
The Prishchepov groups $P(r,n,k,s,q)$ form a broad class of cyclically presented groups. We verify a conjectural characterisation of the perfect groups in this family. We first prove the conjecture for the case $\gcd(n,6)=1$ and then establish further cases beyond this coprimality condition. Consequently, we obtain a classification of perfect Prishchepov groups in a broad range of parameters.
We classify all additive invariants of open Petri nets: these are $\mathbb{N}$-valued invariants which are additive with respect to sequential and parallel composition of open Petri nets. In particular, we prove two classification theorems: one for open Petri nets and one for monically open Petri nets (i.e. open Petri nets whose interfaces are specified by monic maps). Our results can be summarized as follows. The additive invariants of open Petri nets are completely determined by their values on a particular class of single-transition Petri nets. However, for monically open Petri nets, the additive invariants are determined by their values on transitionless Petri nets and all single-transition Petri nets. Our results confirm a conjecture of John Baez (stated during the AMS' 2022 Mathematical Research Communities workshop).
In this paper we finish our classification of nilpotent symplectic alternating algebras of dimension 10 over any field F.
In this paper and its sequel we continue our study of nilpotent symplectic alternating algebras. In particular we give a full classification of such algebras of dimension $10$ over any field. It is known that symplectic alternating algebras over $\mbox{GF}(3)$ correspond to a special rich class $\mathcal{C}$ of $2$-Engel $3$-groups of exponent $27$ and under this correspondence we will see that the nilpotent algebras correspond to a subclass of $\mathcal{C}$ that are those groups in $\mathcal{C}$ that have an extra group theoretical property that we refer to as being powerfully nilpotent and can be described also in the context of $p$-groups where $p$ is an arbitrary prime.
The structure of nilpotent symplectic algebras of maximal class has been studied in [8, 5]. In this paper, we study the dual subclass of algebras of minimal class. In particular, we show that symplectic alternating algebras of dimension up to $16$ that are minimal, in the sense that they are of rank $2$ with minimum nilpotency class, have a class that confirm a conjecture that has been raised in [3].
We develop a structure theory for nilpotent symplectic alternating algebras.