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GROUPS WHOSE PROPER SUBGROUPS OF INFINITE RANK HAVE FINITE CONJUGACY CLASSES
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 89 / Issue 1 / February 2014
- Published online by Cambridge University Press:
- 11 February 2013, pp. 41-48
- Print publication:
- February 2014
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- Article
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A group
$G$ is said to be an 
$FC$-group if each element of 
$G$ has only finitely many conjugates, and 
$G$ is minimal non
$FC$ if all its proper subgroups have the property 
$FC$ but 
$G$ is not an 
$FC$-group. It is an open question whether there exists a group of infinite rank which is minimal non
$FC$. We consider here groups of infinite rank in which all proper subgroups of infinite rank are 
$FC$, and prove that in most cases such groups are either 
$FC$-groups or minimal non
$FC$.
Supersimple ω-categorical groups and theories
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- Journal:
- The Journal of Symbolic Logic / Volume 65 / Issue 2 / June 2000
- Published online by Cambridge University Press:
- 12 March 2014, pp. 767-776
- Print publication:
- June 2000
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