Published February 2016
| Submitted
Journal Article
Open
On matching property for groups and field extensions
- Creators
- Aliabadi, Mohsen
- Hadian, Majid
- Jafari, Amir
Abstract
In this paper we prove a sufficient condition for the existence of matchings in arbitrary groups and its linear analogue, which lead to some generalizations of the existing results in the theory of matchings in groups and central extensions of division rings. We introduce the notion of relative matchings between arrays of elements in groups and use this notion to study the behavior of matchable sets under group homomorphisms. We also present infinite families of prime numbers p such that ℤ/pℤ does not have the acyclic matching property. Finally, we introduce the linear version of acyclic matching property and show that purely transcendental field extensions satisfy this property.
Additional Information
© 2015 World Scientific Publishing Company. Received 15 August 2014; Accepted 3 January 2015; Published 18 August 2015. We would like to thank Professor Noga Alon for his useful suggestions and comments. We would also like to thank the referee for making several useful comments.Attached Files
Submitted - matching.pdf
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Additional details
- Eprint ID
- 60703
- DOI
- 10.1142/S0219498816500110
- Resolver ID
- CaltechAUTHORS:20151002-111244884
- Created
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2015-10-02Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field