On embedding of groups with certain additional properties

Abstract: A group $G$ is said to be embeddable into some group $H$, if there is an injective homomorphism $\varphi: G \to H$, or in other words, $H$ contains an isomorphic copy $G'$ of the group $G$. Our objective is to discuss certain special types of embeddings, such as, embeddings into finitely generated groups, verbal embeddings, embeddings of recursive groups, etc. Reflecting a problem about the explicit embedding of the additive group of rational numbers $\mathbb Q$ from 1990's we display an explicit embedding of $\mathbb Q$ into a finitely presented group.

Mathematics

Audience: undergraduates

( video )

Comments: This is a joint event of the "Yerevan Mathematical Colloquium" and of the "Group Theory Seminar" at the Yerevan State University.

Talk host: Arman Darbinyan (University of Southampton)

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Yerevan Mathematical Colloquium

Series comments: "Yerevan Mathematical Colloquium" invites survey talks aimed at a general mathematical audience, that emphasize proof methods, relations between branches of mathematics, possible applications, and open problems.

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