Symmetric groups are rational-representation
From Groupprops
This article gives the statement, and possibly proof, of a particular group or type of group (namely, Symmetric group (?)) satisfying a particular group property (namely, Rational-representation group (?)).
Contents
Statement
Let be a natural number. The symmetric group of degree
is a Rational-representation group (?): all its representations over the complex numbers can be realized over the field of rational numbers.
Related facts
Weaker facts
Related facts about alternating groups
- Classification of ambivalent alternating groups
- Finitary alternating group on infinite set is ambivalent