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A survey of Schreier-type extensions of monoids

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Abstract

We give an overview of a number of Schreier-type extensions of monoids and discuss the relation between them. We begin by discussing the characterisations of split extensions of groups, extensions of groups with abelian kernel and finally non-abelian group extensions. We see how these characterisations may be immediately lifted to Schreier split extensions, special Schreier extensions and Schreier extensions respectively. Finally, we look at weakenings of these Schreier extensions and provide a unified account of their characterisation in terms of relaxed actions.

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  1. Department of Pure Mathematics and Statistical Sciences, University of Cambridge, Cambridge, UK

    Peter F. Faul

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  1. Peter F. Faul
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Correspondence to Peter F. Faul.

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Communicated by Mark V. Lawson.

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Faul, P.F. A survey of Schreier-type extensions of monoids. Semigroup Forum 104, 519–539 (2022). https://doi.org/10.1007/s00233-022-10265-7

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