Araştırma Makalesi


DOI :10.26650/ijmath.2024.00014   IUP :10.26650/ijmath.2024.00014    Tam Metin (PDF)

A note on vanishing elements and co-degrees of strongly monolithic characters of finite groups

Sultan Bozkurt GüngörGamze AkarTemha Erkoç

Character theory of finite groups have an important role in understanding the structure of finite groups. A number of previously unresolved problems related to the structure of finite groups have been solved with the development of representation and character theory. There are many articles in the literature on the relationships between the structure of finite groups and their irreducible characters. Today, many researchers continue to study these relationships. Our purpose in this paper is to prove that for determining some properties of the structure of a finite group 𝐺, it is enough to consider only strongly monolithic characters of 𝐺 instead of all irreducible characters of 𝐺. We give relationships between the structure of 𝐺 and the vanishing elements, co-degrees of strongly monolithic characters of 𝐺.


PDF Görünüm

Referanslar

  • Berkovich, Y., G., Zhmud’, E., M., 1997, Characters of Finite Groups, Part 2, Translations of Mathematical Monographs, Vol. 181, American Mathematical Society. google scholar
  • Bianchi, M., Chillag, D., Lewis, M.L., Pacifici, E., Character degree graphs that are complete graphs, 2007, Proc. Amer. Math. Soc., 135(3), 671-676. google scholar
  • Chen, X., Yang, Y., Normal p-complements and monomial characters, 2020, Mon.Math. 19, 807-810. google scholar
  • Chillag, D., Herzog, M., On character degrees quotients, 1990, Arch. Math. 55, 25-29. google scholar
  • Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A., Wilson, R. A., 1985, Atlas of Finite Groups, Oxford: Clarendon Press. google scholar
  • Dolfi, S., Navarro, G., Pacifici, E., Sanus L., Tiep P.H., Non-vanishing elements of finite groups, 2010, Journal of Algebra, 323, 540-545. google scholar
  • Erkoç, T., Bozkurt Güngör, S., Özkan, J.M., Strongly Monolithic Characters of Finite Groups, 2023, Journal of Algebra and Its Applications, 22(8), 2350176. google scholar
  • Erkoç, T., Bozkurt Güngör, S., Akar, G., SM-vanishing conjugacy classes of finite groups, 2023, Journal of Algebra and Its Applications, https://doi.org/10.1142/S0219498825500471. google scholar
  • Gallagher, P., X., Group characters and normal Hall subgroups, 1962, Nagoya Math. J. , 21, 223-230. google scholar
  • Herzog M., On finite simple groups of order divisible by three primes only, 1968, Journal of Algebra, 10(3), 383-388. google scholar
  • Huppert, B. , 1967, Endliche Gruppen I, Springer-Verlag, Berlin Heidelberg New York. google scholar
  • Isaacs, I.M. , 1976, Character Theory of Finite Groups, Academic Press, New York. google scholar
  • Isaacs, I.M., Navarro, G., Wolf, T.R., , Journal of Algebra, Finite group elements where no irreducible character vanishes, 1999, Journal of Algebra, 222, 413-423. google scholar
  • Pang, L., Lu, J., Finite groups and degrees of irreducible monomial characters, 2016, Journal of Algebra and its Aplications, Vol. 15, No. 4 1650073. google scholar
  • Qian, G., Wang, Y., Wei, H., Co-degrees of irreducible characters in finite groups, 2007, J. Algebra 312, 946-955. google scholar
  • Robati, S., M., Groups whose set of vanishing elements is the union of at most three conjugacy classes, 2019, Bull. Belg. Math. Soc. Simon Stevin, 26(1), 85-89. google scholar

Atıflar

Biçimlendirilmiş bir atıfı kopyalayıp yapıştırın veya seçtiğiniz biçimde dışa aktarmak için seçeneklerden birini kullanın


DIŞA AKTAR



APA

Bozkurt Güngör, S., Akar, G., & Erkoç, T. (2024). A note on vanishing elements and co-degrees of strongly monolithic characters of finite groups. Istanbul Journal of Mathematics, 2(1), 39-43. https://doi.org/10.26650/ijmath.2024.00014


AMA

Bozkurt Güngör S, Akar G, Erkoç T. A note on vanishing elements and co-degrees of strongly monolithic characters of finite groups. Istanbul Journal of Mathematics. 2024;2(1):39-43. https://doi.org/10.26650/ijmath.2024.00014


ABNT

Bozkurt Güngör, S.; Akar, G.; Erkoç, T. A note on vanishing elements and co-degrees of strongly monolithic characters of finite groups. Istanbul Journal of Mathematics, [Publisher Location], v. 2, n. 1, p. 39-43, 2024.


Chicago: Author-Date Style

Bozkurt Güngör, Sultan, and Gamze Akar and Temha Erkoç. 2024. “A note on vanishing elements and co-degrees of strongly monolithic characters of finite groups.” Istanbul Journal of Mathematics 2, no. 1: 39-43. https://doi.org/10.26650/ijmath.2024.00014


Chicago: Humanities Style

Bozkurt Güngör, Sultan, and Gamze Akar and Temha Erkoç. A note on vanishing elements and co-degrees of strongly monolithic characters of finite groups.” Istanbul Journal of Mathematics 2, no. 1 (Dec. 2024): 39-43. https://doi.org/10.26650/ijmath.2024.00014


Harvard: Australian Style

Bozkurt Güngör, S & Akar, G & Erkoç, T 2024, 'A note on vanishing elements and co-degrees of strongly monolithic characters of finite groups', Istanbul Journal of Mathematics, vol. 2, no. 1, pp. 39-43, viewed 22 Dec. 2024, https://doi.org/10.26650/ijmath.2024.00014


Harvard: Author-Date Style

Bozkurt Güngör, S. and Akar, G. and Erkoç, T. (2024) ‘A note on vanishing elements and co-degrees of strongly monolithic characters of finite groups’, Istanbul Journal of Mathematics, 2(1), pp. 39-43. https://doi.org/10.26650/ijmath.2024.00014 (22 Dec. 2024).


MLA

Bozkurt Güngör, Sultan, and Gamze Akar and Temha Erkoç. A note on vanishing elements and co-degrees of strongly monolithic characters of finite groups.” Istanbul Journal of Mathematics, vol. 2, no. 1, 2024, pp. 39-43. [Database Container], https://doi.org/10.26650/ijmath.2024.00014


Vancouver

Bozkurt Güngör S, Akar G, Erkoç T. A note on vanishing elements and co-degrees of strongly monolithic characters of finite groups. Istanbul Journal of Mathematics [Internet]. 22 Dec. 2024 [cited 22 Dec. 2024];2(1):39-43. Available from: https://doi.org/10.26650/ijmath.2024.00014 doi: 10.26650/ijmath.2024.00014


ISNAD

Bozkurt Güngör, Sultan - Akar, Gamze - Erkoç, Temha. A note on vanishing elements and co-degrees of strongly monolithic characters of finite groups”. Istanbul Journal of Mathematics 2/1 (Dec. 2024): 39-43. https://doi.org/10.26650/ijmath.2024.00014



ZAMAN ÇİZELGESİ


Gönderim22.05.2024
Kabul15.06.2024
Çevrimiçi Yayınlanma25.06.2024

LİSANS


Attribution-NonCommercial (CC BY-NC)

This license lets others remix, tweak, and build upon your work non-commercially, and although their new works must also acknowledge you and be non-commercial, they don’t have to license their derivative works on the same terms.


PAYLAŞ




İstanbul Üniversitesi Yayınları, uluslararası yayıncılık standartları ve etiğine uygun olarak, yüksek kalitede bilimsel dergi ve kitapların yayınlanmasıyla giderek artan bilimsel bilginin yayılmasına katkıda bulunmayı amaçlamaktadır. İstanbul Üniversitesi Yayınları açık erişimli, ticari olmayan, bilimsel yayıncılığı takip etmektedir.