Artin Exponent and CC-Subgroups of Rational Groups

Abstract

A finite group whose irreducible complex characters are rational valued is called a rational group. We prove that if a rational group G contains a CC-subgroup or G is a direct product of Frobenius rational groups, then every rationally represented character is a generalized permutation character.

Key Words:

• Artin exponent
• CC-subgroup
• Local splitting
• Rational group

2010 Mathematics Subject Classification:

• 20C15

ACKNOWLEDGMENT

The author would like to express his deep gratitude to the referee for his/her extensive comments which made it possible to present the paper in this final form.

Notes

Communicated by L. Small.