On 2 February 1932, Alan Don, chaplain to the Archbishop of Canterbury Cosmo Gordan Lang, recorded in his diary the simple entry: ‘Church Assembly – not very invigorating’.1 This has been the tenor of the relationship between the English and the governing bodies of the church for centuries. This article seeks to describe the role of synodality at the regional level2 by reference to the General Synod of the Church of England, with a brief comparative study of the tikanga system in New Zealand, and asks the question whether the procedures meet the expectation of synodality.

The first item of business at the February group of sessions was to revive the General Synod (Remote Meetings) (Temporary Standings Orders) Measure 2020, which enabled Synod to conduct hybrid meetings. Previously in operation during the COVID-19 pandemic, the standing order had lapsed and was brought back into operation until 5 February 2026.

This report covers the group of sessions held in July 2022. General Synod met in York for the first time since the pandemic between 8 and 12 July 2022.

This report covers the groups of sessions held in April and July 2021. Due to the ongoing COVID-19 pandemic, General Synod did not meet formally in February.

Let p and q be distinct primes. We characterize transitive groups G that admit a complete block system of q blocks of size p such that the subgroup of G which fixes each block set-wise has a Sylow p-subgroup of order p. Using this result, we prove that the full automorphism group of a metacirculant graph Γ of order pq such that Aut(Γ) is imprimitive, is contained in one of several families of transitive groups. As the automorphism groups of vertex-transitive graphs of order pq that are primitive have been determined by several authors, this result implies that automorphism groups of vertex-transitive graphs of order pq are known. We also determine all nonnormal Cayley graphs of order pq, and all 1/2-transitive graphs of order pq.

We show that, if G is a graph of order n with maximal degree Δ(G) and minimal degree δ(G) whose complement contains no K2,s, s [ges ] 2, then G contains every tree T of order n−s+1 whose maximal degree is at most Δ(G) and whose vertex of second-largest degree is at most δ(G). We then show that this result implies that special cases of two conjectures are true. We verify that the Erdös–Sós conjecture, which states that a graph whose average degree is larger than k−1 contains every tree of order k+1, is true for graphs whose complement does not contain a K2,4, and the Komlós–Sós conjecture, which states that every graph of median degree at least k contains every tree of order k+1, is true for graphs whose complement does not contain a K2,3.

Mycotoxins are secondary metabolites produced by many phytopathogenic and food spoilage fungi including Penicillium, Fusarium and Aspergillus. The toxicity and carcinogenicity of many of these mycotoxins, and their potential to contaminate foods and animal feedstuffs is a cause of serious concern globally, both from a food safety and food trade standpoint. Thus the rapid identification of mycotoxigenic fungi would be desirable, such that early intervention steps could be applied to help limit the amounts of contaminated materials, particularly cereals and cereal-based products, gaining access to the human food chain. With this in mind a number of PCR-based methodologies have been developed for the identification of mycotoxin biosynthetic genes in different fungal genera, together with assays developed using other genes or random amplification of polymorphic DNA (RAPD) methodologies for the identification of specific toxigenic fungi. In addition, reverse transcription (RT)-PCR, competitive PCR and Real Time quantitative PCR methodologies have also been developed for this purpose. The development of each of these techniques, their usefulness, limitations and adaptability will be discussed together with descriptions of specific examples where these techniques have been utilised in different experimental settings.

Let c [les ] 0.076122 and T1, T2,…, Tn be a sequence of trees such that [mid ]V(Ti)[mid ] [les ] i−c(i−1). We prove that, if for each 1 [les ] i [les ] n there exists a vertex xi ∈ V(Ti) such that Ti−xi has at least (1−2c)(i−1) isolated vertices, then T1,…, Tn can be packed into Kn. We also prove that if T is a tree of order n+1−c′n, c′ [les ] 1/25(37−8 √21) ≈ 0.0135748, such that there exists a vertex x ∈ V(T) and T−x has at least n(1−2c′) isolated vertices, then 2n+1 copies of T may be packed into K2n+1.

In this paper, we solve the isomorphism problem for metacirculant graphs of order $pq$ that are not circulant. To solve this problem, we first extend Babai’s characterization of the $\text{CI}$ -property to non-Cayley vertex-transitive hypergraphs. Additionally, we find a simple characterization of metacirculant Cayley graphs of order $pq$ , and exactly determine the full isomorphism classes of circulant graphs of order $pq$ .