Armeanu, Ion About ambivalent groups. (English) Zbl 0867.20006 Ann. Math. Blaise Pascal 3, No. 2, 17-22 (1996). 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. Cited in 2 Documents MSC: 20C15 Ordinary representations and characters 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks Keywords:real valued characters; ambivalent solvable groups; ambivalent groups; Abelian Sylow 2-subgroups PDF BibTeX XML Cite \textit{I. Armeanu}, Ann. Math. Blaise Pascal 3, No. 2, 17--22 (1996; Zbl 0867.20006) Full Text: DOI Numdam EuDML References: [1] Hupert, B., Blackburn, N., Finite Groups, Vol. 2, Springer Verlag, 1982. · Zbl 0477.20001 [2] Feit, W., Seitz, G.On finite rational groups and related topics, Illinois J. of Mathematics, Vol. 33, no. 1, 1988, (103-131). · Zbl 0701.20005 [3] Isaacs, I.M., Character Theory of Finite Groups, Academic Press, 1976. · Zbl 0337.20005 [4] Rose, J.S., A Course in Group Theory, Cambridge, 1978. · Zbl 0371.20001 [5] Suzuki, M., Group Theory, Vol. 2, Springer Verlag, 1986. · Zbl 0586.20001 [6] Walter, J.H., The characterization of finite groups with abelian Sylow 2-subgroups, Ann. of Math., 89 (1969) 405-514. · Zbl 0184.04605 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.