Rational group

Definition
There are a number of other equivalent definitions that can be used in the case that we are dealing with a finite rational group.

Examples

 * All symmetric groups are rational groups.
 * The finitary alternating group on an infinite set is a rational group.
 * The dihedral groups of degrees $$1,2,3,4,6$$ are rational groups.

Here is a list of examples of small order:

Conjunction with other properties
Hegedűs Pál proved in 2004, the following results: "In this paper it is proved that in a solvable rational group the Sylow 5-subgroup is always normal and elementary Abelian. Moreover, the structure of rational {2, 5}-groups is described in detail."