A Note on the Rational Non-linear Characters of Groups

M. Norooz-Abadian | Hesameddin Sharifi

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=116895
Date :  2019/08/27
Publish in :    Algebras and Representation Theory
DOI :  https://doi.org/10.1007/s10468-019-09920-5
Link :  http://dx.doi.org/10.1007/s10468-019-09920-5
Keywords :Rational valued non-linear characters, Frobenius group

Abstract :

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We study finite groups with rational valued non-linear characters and obtain the structureof these types of groups with derived subgroup of prime order. In particular, in the case ofthe size of derived subgroup of a group is two we conclude that this group is rational if andonly if the group is a direct product of an extraspecial 2-group with an elementary abelian2-group.