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Keywords:
character degree; Huppert's conjecture
Summary:
We improve a few results related to Huppert's $\rho $-$\sigma $ conjecture. We also generalize a result about the covering number of character degrees to arbitrary finite groups.
References:
[1] Bellotti, C., Keller, T. M., Trudgian, T. S.: New bounds for numbers of primes in element orders of finite groups. Available at https://arxiv.org/abs/2211.05837 (2022), 6 pages. DOI 10.48550/arXiv.2211.05837
[2] Hung, N. N., Yang, Y.: On the prime divisors of element orders. Math. Nachr. 294 (2021), 1905-1911. DOI 10.1002/mana.202000249 | MR 4371273 | Zbl 07750808
[3] Keller, T. M.: A linear bound for $\rho(n)$. J. Algebra 178 (1995), 643-652. DOI 10.1006/jabr.1995.1370 | MR 1359907 | Zbl 0859.20014
[4] Liu, Y.: On covering number of groups with trivial Fitting subgroup. Acta Math. Sin., Engl. Ser. 38 (2022), 1277-1284. DOI 10.1007/s10114-022-0521-z | MR 4454357 | Zbl 1495.20003
[5] Manz, O., Wolf, T. R.: Representations of Solvable Groups. London Mathematical Society Lecture Notes Series 185. Cambridge University Press, Cambridge (1993). DOI 10.1017/CBO9780511525971 | MR 1261638 | Zbl 0928.20008
[6] Moretó, A.: On the number of different prime divisors of element orders. Proc. Am. Math. Soc. 134 (2006), 617-619. DOI 10.1090/S0002-9939-05-08156-6 | MR 2180876 | Zbl 1090.20018
[7] Moretó, A.: Huppert's conjecture for character codegrees. Math. Nachr. 294 (2021), 2232-2236. DOI 10.1002/mana.202000568 | MR 4371296 | Zbl 07747386
[8] Qian, G.: A note on element orders and character codegrees. Arch. Math. 97 (2011), 99-103. DOI 10.1007/s00013-011-0278-6 | MR 2820570 | Zbl 1232.20014
[9] Qian, G., Wang, Y., Wei, H.: Co-degrees of irreducible characters in finite groups. J. Algebra 312 (2007), 946-955. DOI 10.1016/j.jalgebra.2006.11.001 | MR 1127.20009 | Zbl 1127.20009
[10] Shi, W.: Characterization of simple groups using orders and related topics. Adv. Math., Beijing 20 (1991), 135-141. MR 1121552 | Zbl 0732.20007
[11] Yang, Y.: On analogues of Huppert's conjecture. Bull. Aust. Math. Soc. 104 (2021), 272-277. DOI 10.1017/S0004972720001409 | MR 4308143 | Zbl 07394393
[12] Yang, Y., Qian, G.: The analog of Huppert's conjecture on character codegrees. J. Algebra 478 (2017), 215-219. DOI 10.1016/j.jalgebra.2016.12.017 | MR 3621669 | Zbl 1423.20009
[13] Zhang, J.: Arithmetical conditions on element orders and group structure. Proc. Am. Math. Soc. 123 (1995), 39-44. DOI 10.1090/S0002-9939-1995-1239809-1 | MR 1239809 | Zbl 0816.20024
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