Solvable groups having primitive characters of degree two

Burcu Çınarcı; Temha Erkoç

doi:10.15672/hujms.892294

Research Article

Year 2022, Volume: 51 Issue: 1, 228 - 234, 14.02.2022

Burcu Çınarcı Temha Erkoç

https://doi.org/10.15672/hujms.892294

Abstract

Supporting Institution

TÜBİTAK

Project Number

119F295

References

[1] Y. Berkovich, I.M. Isaacs and L. Kazarin, Groups with distinct monolithic character degrees, J. Algebra 216, 448-480, 1999.
[2] Y.G. Berkovich and E.M. Zhmud, On Isaacs’ three character degrees theorem, Proc. Am. Math. Soc. 125 (3), 669-677, 1997.
[3] Y.G. Berkovich and E.M. Zhmud, Characters of Finite Groups Part 2, American Mathematical Society, 1999.
[4] T. Erkoç and B. Çınarcı, Monolithic characters of real groups, Comm. Algebra 49 (8), 3192-3199, 2021.
[5] T. Erkoç and B. Çınarcı, Finite solvable groups with few imprimitive irreducible characters, J. Algebra Appl. 2020. https://doi.org/10.1142/S0219498822500669.
[6] I.M. Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976.
[7] O. Manz and T.R. Wolf, Representations of Solvable Groups, London Mathematical Society Lecture Note Series 185, Cambridge University Press, Cambridge, 1993.
[8] G.M. Seitz, Finite groups having only one irreducible representation of degree greater than one, Proc. Am. Math. Soc. 19, 459-461, 1968.

Solvable groups having primitive characters of degree two

Year 2022, Volume: 51 Issue: 1, 228 - 234, 14.02.2022

Burcu Çınarcı Temha Erkoç

https://doi.org/10.15672/hujms.892294

Abstract

In this paper, we are interested in the classification of finite solvable groups having primitive characters of degree two. We first determine all finite solvable groups having both a faithful primitive character of degree two and a faithful real-valued irreducible character. Then we classify all finite solvable groups having at most five nonlinear monolithic characters one of which is primitive of degree two.

Keywords

Solvable groups, Primitive characters, Monolithic characters, Real-valued Character

Project Number

119F295

References

[1] Y. Berkovich, I.M. Isaacs and L. Kazarin, Groups with distinct monolithic character degrees, J. Algebra 216, 448-480, 1999.
[2] Y.G. Berkovich and E.M. Zhmud, On Isaacs’ three character degrees theorem, Proc. Am. Math. Soc. 125 (3), 669-677, 1997.
[3] Y.G. Berkovich and E.M. Zhmud, Characters of Finite Groups Part 2, American Mathematical Society, 1999.
[4] T. Erkoç and B. Çınarcı, Monolithic characters of real groups, Comm. Algebra 49 (8), 3192-3199, 2021.
[5] T. Erkoç and B. Çınarcı, Finite solvable groups with few imprimitive irreducible characters, J. Algebra Appl. 2020. https://doi.org/10.1142/S0219498822500669.
[6] I.M. Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976.
[7] O. Manz and T.R. Wolf, Representations of Solvable Groups, London Mathematical Society Lecture Note Series 185, Cambridge University Press, Cambridge, 1993.
[8] G.M. Seitz, Finite groups having only one irreducible representation of degree greater than one, Proc. Am. Math. Soc. 19, 459-461, 1968.

There are 8 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Mathematics
Authors	Burcu Çınarcı 0000-0003-1202-0968 Temha Erkoç 0000-0001-5437-3679
Project Number	119F295
Publication Date	February 14, 2022
Published in Issue	Year 2022 Volume: 51 Issue: 1

Cite

APA	Çınarcı, B., & Erkoç, T. (2022). Solvable groups having primitive characters of degree two. Hacettepe Journal of Mathematics and Statistics, 51(1), 228-234. https://doi.org/10.15672/hujms.892294
AMA	Çınarcı B, Erkoç T. Solvable groups having primitive characters of degree two. Hacettepe Journal of Mathematics and Statistics. February 2022;51(1):228-234. doi:10.15672/hujms.892294
Chicago	Çınarcı, Burcu, and Temha Erkoç. “Solvable Groups Having Primitive Characters of Degree Two”. Hacettepe Journal of Mathematics and Statistics 51, no. 1 (February 2022): 228-34. https://doi.org/10.15672/hujms.892294.
EndNote	Çınarcı B, Erkoç T (February 1, 2022) Solvable groups having primitive characters of degree two. Hacettepe Journal of Mathematics and Statistics 51 1 228–234.
IEEE	B. Çınarcı and T. Erkoç, “Solvable groups having primitive characters of degree two”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 1, pp. 228–234, 2022, doi: 10.15672/hujms.892294.
ISNAD	Çınarcı, Burcu - Erkoç, Temha. “Solvable Groups Having Primitive Characters of Degree Two”. Hacettepe Journal of Mathematics and Statistics 51/1 (February 2022), 228-234. https://doi.org/10.15672/hujms.892294.
JAMA	Çınarcı B, Erkoç T. Solvable groups having primitive characters of degree two. Hacettepe Journal of Mathematics and Statistics. 2022;51:228–234.
MLA	Çınarcı, Burcu and Temha Erkoç. “Solvable Groups Having Primitive Characters of Degree Two”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 1, 2022, pp. 228-34, doi:10.15672/hujms.892294.
Vancouver	Çınarcı B, Erkoç T. Solvable groups having primitive characters of degree two. Hacettepe Journal of Mathematics and Statistics. 2022;51(1):228-34.