هم درجه سرشت‌های تحویل‌ناپذیر و حقیقی مقدار گروه‌های متناهی

نوع مقاله : مقاله پژوهشی

نویسنده

دانشکده ریاضی و علوم کامپیوتر، دانشگاه صنعتی امیرکبیر، تهران

چکیده

در این مقاله نشان می‌دهیم اگر هم درجه هر سرشت تحویل‌ناپذیر و حقیقی مقدار گروه متناهی $G$ یک $ 2$-عدد یا یک $2'$-عدد باشد، آنگاه $ G$ حلپذیر است.

کلیدواژه‌ها

موضوعات


[1] N. Ahanjideh, The fitting subgroup, p-length derived length and charcter table, Math. Nach., 294 (2021) 214-223.
[2] F. Alizadeh et al., Groups with few codegrees of irreducible characters, Comm. Algebra, 47 (2019) 1147–1152.
[3] Z. Akhlaghi, Real elements and real-valued irreducible character codegree, Submitted.
[4] R. Bahramian and N. Ahanjideh, p-divisibility of co-degrees of irreducible characters, Bull. Austral. Math. Soc., 103 (2021) 78–82.
[5] M. Bianchi, D. Chillag, M. L. Lewis and E. Pacifici, Character degree graphs that are complete graphs, Proc. Amer. Math. Soc., 135 (2007) 671–676.
[6] L. Bonazzi, Finite non-solvable groups whose real degrees are prime powers, J. Group Theory, 25 (2022) 741–751.
[7] D. Chillag, A. Mann and O. Manz, The co-degrees of irreducible characters, Israel J. Math., 73 (1991) 207–223.
[8] I. Isaacs, Element orders and character codegrees, Arch. Math. (Basel), 97 (2011) 499–501.
[9] G. Navarro and P. H. Tiep, Rational irreducible characters and rational conjugacy classes in finite groups, Trans. Amer. Math. Soc., 360 (2008) 2443–2465.
[10] G. Navarro, L. Sanus and P. H. Tiep, Real characters and degrees, Israel J. Math., 171 (2009) 157–173.
[11] G. Navarro and P. H. Tiep, Degrees of rational characters of finite groups, Adv. Math., 224 (2010) 1121–1142.
[12] G. Qian, A note on element orders and character codegrees, Arch. Math. (Basel), 97 (2011) 99–103.
[13] G. Qian, Elemment orders and character codegrees, Bull. London Math. Soc., 53 (2021) 820–824.
[14] G. Qian, Y. Wang and H. Wei, Codegree of irreducible characters in finite groups, J. Algebra, 312 (2007) 946–955.