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Bianchi, Mariagrazia, Herzog, Marcel. (1397). Finite groups with non-trivial intersections of kernels of all but one irreducible characters. , 7(3), 63-80. doi: 10.22108/ijgt.2017.21609
Mariagrazia Bianchi; Marcel Herzog. "Finite groups with non-trivial intersections of kernels of all but one irreducible characters". , 7, 3, 1397, 63-80. doi: 10.22108/ijgt.2017.21609
Bianchi, Mariagrazia, Herzog, Marcel. (1397). 'Finite groups with non-trivial intersections of kernels of all but one irreducible characters', , 7(3), pp. 63-80. doi: 10.22108/ijgt.2017.21609
Bianchi, Mariagrazia, Herzog, Marcel. Finite groups with non-trivial intersections of kernels of all but one irreducible characters. , 1397; 7(3): 63-80. doi: 10.22108/ijgt.2017.21609

Finite groups with non-trivial intersections of kernels of all but one irreducible characters

International Journal of Group Theory
مقاله 5، دوره 7، شماره 3، آذر 2018، صفحه 63-80    اصل مقاله (236.82 K)
نوع مقاله: Ischia Group Theory 2016
شناسه دیجیتال (DOI): 10.22108/ijgt.2017.21609
نویسندگان
Mariagrazia Bianchi* 1؛ Marcel Herzog2
1Dipartimento di Matematica quot;Federigo Enriques quot;, Università di Milano
2Schoool of Mathematical Sciences, Tel-Aviv University
چکیده
In this paper we consider finite groups $G$ satisfying the following‎ ‎condition‎: ‎$G$ has two columns in its character table which differ by exactly one‎ ‎entry‎. ‎It turns out that such groups exist and they are exactly the finite groups‎ ‎with a non-trivial intersection of the kernels of all but one irreducible‎ ‎characters or‎, ‎equivalently‎, ‎finite groups with an irreducible character‎ ‎vanishing on all but two conjugacy classes‎. ‎We investigate such groups‎ ‎and in particular we characterize their subclass‎, ‎which properly contains‎ ‎all finite groups with non-linear characters of distinct degrees‎, ‎which were characterized by Berkovich‎, ‎Chillag and Herzog in 1992‎.
کلیدواژه‌ها
‎Finite groups؛ Complex characters
مراجع
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[4] S. Dolfi and M. K. Yadav, Finite groups whose non-linear irreducible characters of the same degree are Galois conjugate, J. Algebra, 452 (2016) 1–16.

[5] W. Feit, Characters of finite groups, W. A. Benjamin Inc., New York-Amsterdam, 1967.

[6] S. S. Gagola, Characters vanishing on all but two conjugacy classes, Pacific J. Math., 109 (1983) 363–385.

[7] M. Hall, The theory of groups, AMS Chelsea Publishing, Providence, Rhode Island, 1999.

[8] B. Huppert, Character theory of finite groups, Walter de Gruyter, Berlin, 1998.

[9] M. Loukaki, On distinct character degrees, Israel J. Math., 159 (2007) 93–107.

[10] D. Passman, Permutation groups, W. A. Benjamin Inc., New York-Amsterdam, 1968.

[11] G. Seitz, Finite groups having only one irreducible representation of degree greater than one, Proc. Amer. Math. Soc., 19 (1968) 459–461.

[12] H. Zassenhaus, Kennzeichnung endlicher linear Gruppen als Permutationsgruppen, Hamburg Abh., 11 (1936) 17–40.

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