Homogeneous structures with nonuniversal automorphism groups
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00538864" target="_blank" >RIV/67985840:_____/20:00538864 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/jsl.2020.10" target="_blank" >https://doi.org/10.1017/jsl.2020.10</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/jsl.2020.10" target="_blank" >10.1017/jsl.2020.10</a>
Alternative languages
Result language
angličtina
Original language name
Homogeneous structures with nonuniversal automorphism groups
Original language description
We present three examples of countable homogeneous structures (also called Fraïssé limits) whose automorphism groups are not universal, namely, fail to contain isomorphic copies of all automorphism groups of their substructures. Our first example is a particular case of a rather general construction on Fraïssé classes, which we call diversification, leading to automorphism groups containing copies of all finite groups. Our second example is a special case of another general construction on Fraïssé classes, the mixed sums, leading to a Fraïssé class with all finite symmetric groups appearing as automorphism groups and at the same time with a torsion-free automorphism group of its Fraïssé limit. Our last example is a Fraïssé class of finite models with arbitrarily large finite abelian automorphism groups, such that the automorphism group of its Fraïssé limit is again torsion-free.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA17-27844S" target="_blank" >GA17-27844S: Generic objects</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Symbolic Logic
ISSN
0022-4812
e-ISSN
—
Volume of the periodical
85
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
11
Pages from-to
817-827
UT code for WoS article
000612018200015
EID of the result in the Scopus database
2-s2.0-85100137732