Chernikov group
A Chernikov group is a group $G$ that has a normal subgroup^{} $N$ such that $G/N$ is finite and $N$ is a direct product^{} of finitely many quasicyclic groups.
The significance of this somewhat arbitrarylooking definition is that all such groups satisfy the minimal condition, and for a long time they were the only known groups with this property.
Chernikov groups are named after http://wwwgroups.dcs.stand.ac.uk/ history/Biographies/Chernikov.htmlSergei Chernikov, who proved that every solvable group^{} that satisfies the minimal condition is a Chernikov group. We can state this result in the form of the following theorem.
Theorem.
The following are equivalent^{} for a group $G$:

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$G$ is a Chernikov group.

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$G$ is virtually abelian and satisfies the minimal condition.

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$G$ is virtually solvable and satisfies the minimal condition.
Title  Chernikov group 

Canonical name  ChernikovGroup 
Date of creation  20130322 15:48:21 
Last modified on  20130322 15:48:21 
Owner  yark (2760) 
Last modified by  yark (2760) 
Numerical id  8 
Author  yark (2760) 
Entry type  Definition 
Classification  msc 20F50 
Synonym  Černikov group 
Related topic  MinimalCondition 