Let G be a finite group. We show that the order of the subgroup generated by coprime γk-commutators (respectively,δk- commutators) is bounded in terms of the size of the set of coprime γk-commutators (respectively, δk-commutators). This is in parallel with the classical theorem due to Turner-Smith that the words γk and δk are concise.

A group G is n-central if Gn ≤ Z(G), that is the subgroup of G generated by n-powers of G lies in the centre of G. We investigate p k -central groups for p a prime number. For G a finite group of exponent pk , the covering group of G is pk -central. Using this we show that the exponent of the Schur multiplier of G is bounded by p⌈c/p-1⌉, where c is the nilpotency class of G. Next we give an explic

In a previous paper, Button and Thillaisundaram proved that all finitely presented groups of p-deficiency greater than one are p-large. Here we prove that groups with a finite presentation of p-deficiency one possess a finite index subgroup that surjects onto the integers. This implies that these groups do not have Kazhdan's property (T). Additionally, we show that the aforementioned result of But

A p-group G is p-central if Gp ≤ Z(G), and G is p2-abelian if (xy)p2 = xp2 yp2 for all x; y ε G. We prove that for G a finite p2-abelian p-central p-group, excluding certain cases, the order of G divides the order of Aut(G).

We use Schlage-Puchta's concept of p-deficiency and Lackenby's property of p-largeness to show that a group having a finite presentation with p-deficiency greater than 1 is large, which implies that Schlage-Puchta's infinite finitely generated p-groups are not finitely presented. We also show that for all primes p at least 7, any group having a presentation of p-deficiency greater than 1 is GolodS

A global energy transition requires alternatives to fossil fuels in energy-intensive industries and transport sectors, which are particularly reliant on the unique material properties of fossil fuels as fuel and as feedstock. Renewable energy transitions, therefore, demand large-scale investments in green hydrogen to produce substitutes as a means of indirect electrification. In the context of Eur

This article provides some brief reflections on the ideas raised in the special issue on the social dimension of EU trade policies from a normative power (NP) perspective. A NP perspective attempts to understand and judge the ideational aspects of the EU by studying the EU’s principles, actions and impact in world politics. The article first elaborates on the role of labour rights as human rights

The mythology of the European Union (EU) in world politics can be told and untold in many different ways. This article focuses on the lore or stories of who did what to whom, the ideological projection of the past onto the present and the escapist pleasure of storytelling in looking at the mythology of ‘global Europa’– the EU in the world. It concludes with a reflection on the way in which the man

The role of symbolism in European integration provides one way of answering Craig Calhoun's 2003 call in Comparative European Politics for a means of transcending specific regimes of analysis in order to advance European studies. The article argues that our understanding of the integration process and the constitution of the European Union (EU) is furthered by broadly studying symbolic forms in a

The European Union is often compared to other political systems in order to better understand its basic features and how they structure politics. This article argues that this focus on comparative politics instils a domestic bias into the study of the EU, which also ignores the impact of enlargement. To remedy this, a comparison is suggested between the order of the EU as a regional international

This intervention seeks to revivify democratic thinking in political geography, through foregrounding and pluralising its material and temporal dimensions. At the same time, it speaks to a renewed centrality and relevance of infrastructure and infrastructural projects in political discourse. The contributions included here demonstrate how an infrastructural lens can offer new insights into democra

The ubiquity of microplastics ecosystems has gained global attention. In this context, Latin America, which is responsible for 8% of the world's consumption of plastic material and has a small recycling rate (4.5%), does not have enough data on microplastics contamination in its environmental matrices. This systematic review analyzed 196 studies from 16 territorials in Latin America and provided i

Microplastic (MP) contamination is a topic of growing global concern; these particles are ubiquitous in environmental ecosystems and have been found in aquatic, terrestrial, and atmospheric mediums. However, the protocols to quantify MPs in environmental samples have limitations and may lead to overestimation and/or underestimation of the plastic debris. Therefore, the aim of this research was to

Direct photolysis of the emerging contaminant 2-(thiocyanomethylthio) benzothiazole (TMCTB) was performed in aqueous solution at different concentrations with high-pressure mercury lamp (5.0, 8.0, 13.0, 16.0, 20.0, 23.0, 27.0, 35.0, 40.0, 45.0, and 50.0 mg L− 1) and with natural sunlight radiation (6.0, 30.0, and 60.0 mg L− 1). TCMTB underwent rapid degradation by direct photolysis with a high-pre

The ubiquitous presence of microplastics in the aquatic environment has raised concern about their potential impacts on and risks to the biota. While the presence of microplastics in a marine environment has been well studied, the impact of microplastic contamination in freshwater bodies is understudied. In the present study, baseline data about contamination with microplastics in Lake Guaíba in s

Brazil maintains its position at the top of the global ranking of plastic producers, yet recycling efforts have been incipient. Recent data reveals an annual production of approximately 14 million tons of plastic waste, not accounting for the surge in the usage of plastic masks and related materials due to the COVID-19 pandemic. However, what remains largely unreported is that over half of post-co

In this work, Piraíba and Dourada skin wastes were used for leather processing. They were initially stripped and characterized by their percentage composition. The results showed that pH, differential pH cipher [SLC13/ IUC 11/ BS 1309:9 - Determination of pH value and Difference Figure of an Aqueous Extract], chromium content and mechanical properties after chromium tanning were in accord with lea

The current research investigates the removal of endocrine disruptor compounds (EDC) in the absence and presence of organic matter in aqueous solution and natural water. In addition, the interactions of different fractions of natural organic matter (NOM) and fulvic acid (FA) in 17α-estradiol (EE2), 17β-estradiol (E2), estrone (E1) estriol (E3) and bisphenol A (BPA) were assessed. The interaction e

Microbicides in the leather industries are employed to avoid the biodeterioration of the hides by microorganisms. This problem may lead to harmful characteristics to the end product such as stains, roughness and decrease mechanical properties of leather. Therefore, microbicides like the 2-(thiocyanomethylthio) benzothiazole (TMCTB) are applied in distinct steps of the tanning process as alternativ