Existentially and $\kappa$-existentially closed groups

Q: How can I download an article?

To download an article from SID, first log in to the site, search for the article title, and click on the 'Download Article' option.

Q: How can I download an ISI article?

To download an ISI article on SID, enter the keyword or article title in the search bar, view the relevant results, click on the desired article, and select the 'Download Article' option.

Q: How can I access the SID database?

To access the SID database, visit SID.ir, create an account, and log in to access scientific resources.

Q: Is downloading articles from SID free?

Some articles on SID are available for free, while others require payment. Details are specified on the article's page.

Kaya Burak; Kuzucuoglu Mahmut

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF GROUP THEORY Year:2023 | Volume:12 | Issue:1 Page(s): 45-54

Download Full-Text

View:

Download:

Cites:

Information Journal Paper

Title

Existentially and $\kappa$-existentially closed groups

Author(s)

Kaya Burak | Kuzucuoglu Mahmut | Issue Writer Certificate

Keywords

Existentially closed groups

Algebraically Closed Groups

Automorphism Groups

Abstract

A group $G$ is existentially closed (algebraically closed) if every finite system of equations and in-equations that has coefficients in $G$ and has a solution in an overgroup $H\geq G$ has a solution in $G$. Existentially closed groups were introduced by W. R. Scott in 1951. B. H. Neumann posed the following question in 1973: Does there exist explicit examples of Existentially closed groups? Generalized version of this question is as follows: Let $\kappa$ be an infinite cardinal. Does there exist explicit examples of $\kappa$-Existentially closed groups? Recently an affirmative answer was given to Neumann's question and the generalized version of it, by Kaya-Kegel-Kuzucuo\u{g}lu. We give a survey of these results. We also prove that, there are maximal subgroups of $\kappa$-existentially Existentially closed groups and provide some information about subgroups containing the centralizer of subgroups generated by fewer than $\kappa$-elements. This generalizes a result of Hickin-Macintyre.

Multimedia

No record.

Cites

No record.

References

No record.

Cite

Related Journal Papers

No record.

Related Seminar Papers

No record.

Related Plans