Combinatorial Group Theory: COMBINATORIAL GROUP THEORY

Discoveries in finite semigroups have influenced several mathematical fields, including theoretical computer science, tropical algebra via matrix theory with coefficients in semirings, and other areas of modern algebra. This comprehensive, encyclopedic text will provide the reader - from the graduate student to the researcher/practitioner with a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. Key features: (1) Develops q-theory, a new theory that provides a unifying approach to finite semigroup theory via quantization; (2) Contains the only contemporary exposition of the complete theory of the complexity of finite semigroups; (3) Introduces spectral theory into finite semigroup theory; (4) Develops the theory of profinite semigroups from first principles, making connections with spectra of Boolean algebras of regular languages; (5) Presents over 70 research problems, most new, and hundreds of exercises. Additional features: (1) For newcomers, an appendix on elementary finite semigroup theory; (2) Extensive bibliography and index. The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, and thereby updates and modernizes the literature of semigroup theory.

The q-theory of Finite Semigroups

We summarize properties of 3-manifold groups, with a particular focus on the consequences of the recent results of Ian Agol, Jeremy Kahn, Vladimir Markovic and Dani Wise.

3-Manifold Groups

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Syntactic semigroups Jean-Eric Pin

Syntactic semigroups

https://ambio1.leeds.ac.uk/Pure/staff/macpherson/homog7.pdf

A survey of homogeneous structures

Introduction to profinite groups and Galois cohomology

THE PRO-p TOPOLOGY OF A FREE GROUP AND ALGORITHMIC PROBLEMS IN SEMIGROUPS

Profinite Graphs and Groups

In the context of abstract groups and ordinary free products, the analogous results follow easily from the fact that each element of the free product has a normal expression s a finite product of elements from the factor groups. Of course, no such normal form exists for the elements of free profinite products. Our methods use instead, s our main tool, the Kurosh subgroup theorem, which is valid for open subgroups of free profinite products.

Torsion elements and centralizers in free products of profinite groups.

On amalgamated products of profinite groups

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