About ambivalent groups. (English) Zbl 0867.20006

Summary: We prove some properties of the ambivalent groups (an ambivalent group is a group all whose characters are real valued) and completely determine the ambivalent solvable groups with one conjugacy class of involutions. Also we study the structure of the ambivalent groups having abelian Sylow 2-subgroups.


20C15 Ordinary representations and characters
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
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