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- Title
Invariable generation and wreath products.
- Authors
Cox, Charles Garnet
- Abstract
Invariable generation is a topic that has predominantly been studied for finite groups. In 2014, Kantor, Lubotzky and Shalev produced extensive tools for investigating invariable generation for infinite groups. Since their paper, various authors have investigated the property for particular infinite groups or families of infinite groups. A group is invariably generated by a subset š if replacing each element of š with any of its conjugates still results in a generating set for šŗ. In this paper, we investigate how this property behaves with respect to wreath products. Our main work is to deal with the case where the base of GāXH is not invariably generated. We see both positive and negative results here depending on š» and its action on š.
- Subjects
INFINITE groups; FINITE groups; WREATH products (Group theory)
- Publication
Journal of Group Theory, 2021, Vol 24, Issue 1, p79
- ISSN
1433-5883
- Publication type
Article
- DOI
10.1515/jgth-2020-0031