arXiv subjects

Paul Bradley

Publications and source records attributed to Paul Bradley.

3 recordsLinked to original sources

arXiv2021

A Theorem of Siemons and Wagner

In 1988 Siemons and Wagner describe a relationship between the lengths of $G$-orbits on subsets of a $G$-set $Ω$. They highlighted the situation where $Δ\subset Ω$ with $|Δ|=k,$ and $|Δ^G|>|Σ^G|$ for all $(k+1)$-subsets, $Σ$ of $Ω$ where $Δ\subsetΣ$. They went on to classify all primitive groups with this property for $k=2$. Here we address some questions about primitive permutation groups satisfying this property when $k=3$ and list all $3$-homogeneous groups satisfying this condition.

math.GR↗

arXiv2018

Prime Number Sums

We prove that it is always possible to find a permutation $p$ on the set $\{1,...,n\}$ such that $c+p(c)$ is prime for all $c \in \{1,...,n\}.$

math.GR↗

arXiv2017

Python Implementation and Construction of Finite Abelian Groups

Here we present a working framework to establish finite abelian groups in python. The primary aim is to allow new A-level students to work with examples of finite abelian groups using open source software. We include the code used in the implementation of the framework. We also prove some useful results regarding finite abelian groups which are used to establish the functions and help show how number theoretic results can blend with computational power when studying algebra. The groups established are based modular multiplication and addition. We include direct products of cyclic groups meaning the user has access to all finite abelian groups.

math.GR↗